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Not just quantum mechanics

The wave function is also used in radio antenna calculations. (J.K. Raines. "Folded Unipole Antennas..."). When I found this page, I was hoping for a rather more general description of wave functions. I am not interested in the particular application to quantum mechanics. Baruchatta (talk) 18:37, 22 February 2010 (UTC)

Are you looking for wave equations? 18.189.51.204 (talk) 18:18, 5 October 2010 (UTC)

A bit unclear

This page is utterly useless for anyone who isn't doing 3rd year Science degree majoring in quantum mechanics or a PhD thesis. It goes straight onto vectors etc etc, formalities and stuff. But what it doesn't do is describe what exactly the wave function is used for, why do we need it, written in the tone that most people can understand. Remember anyone who can understand this article right now most likely know all this stuff already.

I'm not going to pretend that I am a Science PhD postgrad student, but here my suggestion. Have an introduction that introduces the reader to what a wavefunction exactly is.

"The idea of a wavefunction is derived from the claim that all matter exhibits wave properties (matter wave duality), by Schrodinger's Equation. The form of a wavefunction in quantum mechanics is similar/analogous to any other equation that describes wave or wave-like motion by the relation d^2u/dt^2 = 1/s * d^2u/dx^2. The one dimensional wavefunction is analogous to a wave of a string. The wavefunction is the heart of quantum mechanics as important as forces in classical mechanics."

I know its not worded very well and probably not correct, but this would be sufficient to give your average Engineering student enough to know exactly what the conversation is about the next time he joins a science student conversation. Basicly what the wavefunction does, why do we use it, and what it is for etc, to serve as a 5 line introduction for the non-technical crowd.

Also the intergral at the start of this page is very good too The paragraph that explains it is also fairly decent. EDIT: I see how the integral is down the bottom now, but it would be useful to give your average guy one line refering to that at the top, since that is one of the fundamental properties of the wavefunction. 07:41, 20 February 2008 (UTC) --67.68.88.200 (talk) 02:17, 22 December 2007 (UTC)

RZ heretic 05:21, 28 September 2006 (UTC)

I would hope an average engineering student (other than first year) would know what a vector is, and even what a wave function is. Um, speaking as an engineering graduate from years ago...Sigh, once again I am finding this months after the fact..Jance 02:58, 15 February 2007 (UTC)

The formulae could still use some work. They mean nothing to someone (like me!) who isn't already familiar with them. Could somebody explain the variables? Taking electrical theory as an example, it's not enough to write "V=IR". If you want the layman to even hope to get a grasp of the concept, you have to write "V=IR where V=voltage, I=current and R=resistance". This at least doesn't seem to have been done consistently in the current version of the article. Thanks. — NRen2k5 22:29, 16 October 2007 (UTC)

Agree. This article should be presented in an easier way for regular people with not much training in quantum mechanics.Camilo Sanchez (talk) 08:03, 20 February 2008 (UTC)

Mistake in section "formalism"

Hallo, I think the first part of this section was not correct. The allowed states do not form a vector space, i.e. they do not satisfy the vector space axioms!
Why don't they form a vector space? Example: Consider two allowed (hence normalised) states ${\displaystyle |1\rangle }$ and ${\displaystyle |2\rangle }$. If the allowed states formed a vector space, then ${\displaystyle |1\rangle +|2\rangle }$ would also be an allowed state. But this superposition is not normalised anymore. Nevertheless, the allowed states form a subset of this vector space H, namely the sphere of radius 1.
Therefore, remark (2) was wrong as well. If the allowed states formed a vector space, the zero vector, which leaves all other vectors unaltered under vectorial addition, would also be an allowed state. But the zero vector is not normalised, either! Hence, the zero vector is not element of the subset of allowed states, which therefore does not satisfy this axiom!
I corrected that, but somebody should read through it again and probably correct my language mistakes.
Regards, --Rene () 26. Mar 2006 16.55 (CET)

Something still seems wrong here. If a wave function is required to be normalized (is it?), the condition |a|^2+|b|^2=1 doesn't insure that the linear combination of states is normalized, or even normalizable. E.g. take a=1/√2 and b=-1/√2 and theta=phi. —Preceding unsigned comment added by SeaRisk (talk • contribs) 19:42, 27 January 2010 (UTC)

constraints

This page could use some constraints on possible wavefunctions - like the constraints found here. Fresheneesz 19:49, 15 May 2006 (UTC)

what the hell

i ran into the page by accident, and the version i saw was sloppily written. that's nothing fatal, one can always correct mistakes. but, looking through the history page makes me wanna ask, what happened to this article? going from this to the version i saw is clearly not an improvement. Mct mht 10:25, 30 June 2006 (UTC)

Agreed. It now contains almost no useful information and just a tedious list of formulas. Has other stuff been merged elsewhere? Zocky | picture popups 16:03, 4 July 2006 (UTC)

This was done supposedly to "improve readability" (choke).--CSTAR 16:38, 4 July 2006 (UTC)

This is predominantly pure mathematics and is woefully insufficient insofar as elucidating the fundamental physics of quantum mechanics is concerned. It's completely unreadable to anyone who has studied quantum mechanics but not functional analysis. It has a place on wikipedia, but certainly not under the name "wavefunction." --140.252.24.119 21:54, 12 July 2006 (UTC)

although i don't really agree, that's a fair critique of an article. but it's not sufficient reason to just unilaterally delete stuff, in this case good information, IMHO. if one feels that way, perhaps a better way to proceed would be suggesting the material be relocated or move the page. Mct mht 03:33, 13 July 2006 (UTC)

BTW, current version of article could use some cleaning-up. Mct mht 03:50, 13 July 2006 (UTC)

"However, it is important to note that the wavefunction associated with a system is not uniquely determined by that system, as many different wavefunctions may describe the same physical scenario" refers to things like global gauge invariance, not simply a change of basis. E.g. ${\displaystyle e^{i\Theta ({\vec {x}})}\Psi }$ is physically the same as ${\displaystyle \Psi }$ (it corresponds to a gauge transformation of the electromagnetic potentials). I don't understand why you've deleted it and replaced it with a discussion about bases, which are something completely different.

it was removed because it was a ambiguously worded claim with no explanation. it's a simple statement about one only distinguishes the wave function up to a global phase. a comment like that should, and could easily, be explained further. Mct mht 19:46, 13 July 2006 (UTC)

There are other degrees of freedom in the wavefunction aside from local/global gauge invariance. I suppose an entire section could be created to discuss these, and maybe a refrence made to that section in the area where the text was deleted. --Joshua Barr 21:11, 13 July 2006 (UTC)

Also, "...which describes the state of a physical system by expanding it in terms of other states of the same system" is simply the superposition principle. This statement is actually taken almost word for word out of Dirac's "The Principles of Quantum Mechanics," so it really ought to be restored in some capacity as it is essentially the definition of wavefunction (in the eyes of physicists if not mathematicians). --Joshua Barr 19:03, 13 July 2006 (UTC)

Dirac's exact words, really? well, ok. to be more precise, the superposition principle says the state space is a vector space and a wave function is an element of that space. that comment lends itself to confusion. a wave function is the description of a state. how does expanding it in terms of other states "describe" the state? a comment like should be accompanied with a sensible explanation (expanding in terms of a eigenbasis, etc) Mct mht 19:46, 13 July 2006 (UTC)

Expressing the state of a physical system in terms of other states of the same system is precisely what a wavefunction does. The coordinate basis tells you how to write the state of the system as the superposition of position eigenstates, the phase space representation tells you how to write the state of the system in terms of momentum eigenstates, etc. I understand your criticism (lack of exposition) and I'm sure some elaboration wouldn't hurt, but I really think this is the most important point of the entire article. Without it, people have naive ideas about what a wavefunction is (e.g. they relegate it to a mysterious function related to a probability denisty by the collapse posulate) and they fail to see how, for example, the position representation (continuuous) and the energy representation (typically discrete) are accomplishing precisely the same thing. As far as the vector space axioms are concerned, those are just an element of a mathematican formalism... the superposition principle is something very physical with a valdity independent of any particular formalism. I think this article should avoid emphasizing the formalism (until the section about formalism of course) and be a physical as possible (e.g. in the spirit of the Feynman lectures). Anyways, I am sure we can rework the article to satisfy both our concerns. --Joshua Barr 21:11, 13 July 2006 (UTC)

Also, in response to the criticism that the article is a tedious "list" of equations and so on... I really feel that the best way to convey this material to the people who are likely to be reading it (I wrote this for an audience approximatly on par with a physics student taking their first formal quantum course) is via example and not dense formalism (of course that has its place too). Let's remember that the people reading this aren't typically going to have a degree in mathematics or physics as I and (I assume many of you) do. We can't write this article for simply ourselves; wikipedia is for the masses.--Joshua Barr 21:28, 13 July 2006 (UTC)

No meaning

this page has no meaning because it doesnt give the formula for the wave function

The formula for the wave function grows to several pages long for any system containing more than a few particles. The problem is that it is a recursive simultanious equation. When one reaches the entanglement point it becomes nearly impossible to solve without the aid of computers simply because of the time it would take to write it down. Now the integral generating the wave function, on the other hand, is fairly short and is included. --Scorpion451 01:54, 1 July 2007 (UTC)

I hate to dig this up, but it may answer questions to future viewers. the wavefunction is a solution to a PDE (partial differential equation). such equations are not in the form of X = .... These equations are written in a form that is general, as the schrodinger equation (the form of which determines the solution --> the wavefunction) IS DIFFERENT for every single situation. the equatin is -ihbar dpsi/dt = Hpsi. this is a general equation, relating the time derivative of the wavefunction to the total energy (the hamiltonian), and hence the conjugate relationship of energy and time (fourier pairs), which even leads to the uncertainty principle in time and energy (which only exists because of this relationship). this is the equation. it cannot be accurately or correctly written in any simpler way. it is exceedingly difficult/impossible to solve for all but the most simple situations, and many of the breakthroughs in modern physics concern methods of accurately and quickly approximating the solutions to the schrodinger equation. —Preceding unsigned comment added by 68.6.52.200 (talk) 02:55, 1 March 2009 (UTC)

Why is title one word instead of two ?

I don't recognize "wavefunction" as an English word, but rather two words: "wave function". The title should therefore be changed accordingly. Does everyone agree ? StuRat 18:32, 18 September 2006 (UTC)

Agreed. Waxigloo 20:59, 18 September 2006 (UTC)

Agreed. Jace P 23:00, 01 November 2006

Agreed. That is the usage in the Feynman lectures. Also, I rewrote the intro, to be less chemistry oriented.--agr 14:45, 2 November 2006 (UTC)

If all are agreed, why hasn't anything been done? I'm going to move the page, as that seems to be the consensus. Oh, and "wavefunction" gets more ghits than does "wave function", but "wavefunction" is not in my dictionary. MacGuy 22:42, 12 February 2007 (UTC)

On second thought, I'm not going to move the page until more information is gained on the matter, as not all seem to be agreed. MacGuy 22:53, 12 February 2007 (UTC)

However, compare Google scholar hits "wavefunction" = 108,000 vs. "wave function" = 482,000. − Twas Now ( talk • contribs • e-mail ) 16:56, 14 February 2007 (UTC)

I did a scholarly search using CSA Illumina: General Science Abstracts.

Results for Wavefunction: 53 (peer-reviewed) journals

Results for Wave function: 453 (peer-reviewed) journals

This confirms my initial belief that it was "wave function". − Twas Now ( talk • contribs • e-mail ) 16:43, 14 February 2007 (UTC)

Very good. I'll move the page. MacGuy 14:42, 15 February 2007 (UTC)

Yeah, that looks like the correct thing to do.--AaronM 15:45, 15 February 2007 (UTC)

Actually, an admin will have to do it… Also, what should be done about the title of wavefunction collapse? MacGuy 17:17, 15 February 2007 (UTC)

Well, I am currently in a Modern Physics Course. Everywhere on the class site, the word "wavefunction" is referred to as 1 word. Here is the site: http://electron6.phys.utk.edu/phys240/Modules.asp

I agree. "Wave function" is the older terminology, but nowadays physicists almost always refer to "wavefunction" in the quantum context. --Michael C. Price 23:46, 4 November 2007 (UTC)

Moved

I've moved the page, per the above discussion and the request at WP:RM. It seems that Wavefunction collapse should move as well, huh? I don't see any reason to go through a five-day procedure for that; I'll just move it. -GTBacchus 00:12, 21 February 2007 (UTC)

Ok, that's done, and Normalisable wave function as well. Cheers. -GTBacchus 00:31, 21 February 2007 (UTC)

I think we should think again about this. "Wavefunction collapse" always refers to the quantum case, so we can't just carry over the terminology from "wavefunction" which includes the non-quantum usage. --Michael C. Price 23:50, 4 November 2007 (UTC)

Why only quantum mechanics?

The wave function is also used extensively in fluid mechanics - the tone of the article seems to imply that the field of quantum mechanics somehow "owns" the wave function, which is not the case. —The preceding unsigned comment was added by Rpbigger (talk • contribs) 02:52, 15 February 2007 (UTC).

From my recollection, a wave function is a mathematical solution to a partial differential equation (wave equation)....as in electromagnetism. The wave function is a term (phrase?) used in any number of areas of physics, both classical and quantum mechanics. I am not an expert in fluid mechanics but I surely can understand how it would apply there. While I suspect more people are familiar with the term as it relates to Schrodingers equations/quantum mechanics, you make a valid point. Jance 03:28, 15 February 2007 (UTC)

Good Point - the article probably should be what people are most familliar with. I probably was overstating a bit when I said extensivel - its possible also possible that the idea has been applied on a mathematical basis for certain situations in continuum mechanics after it was developed in quantum theory. Rpbigger 17:11, 15 February 2007 (UTC)

agreed, a wave function is just a solution to a wave equation, it is therefore a mathematical concept (though the term is more commonly used in physics than in mathematics).

I think his topic would benefit from some restructuring to improve clarity and readability. Perhaps this article should contain a brief description of the mathematical concept (including a list of physical applications) and a new page should be made for "quantum wave function". Also, as it is, this article discusses the concept of a "quantum state", including state vectors (which are not wave functions). perhaps the content pertaining to state vectors should be moved to a new article "quantum state vector". --V. 00:08, 16 February 2007 (UTC)

Typo in formula?

In section "Two distinguishable particles in three spatial dimensions", the normalization condition formula is using a psi(x, y, z) function. I think that should be psi(x1, y1, z1, x2, y2, z2). Or maybe just psi, as in the first formula of that section. Either way, they should be the same. Since I know almost nothing of advanced physics or that funny-looking math, I don't dare edit it myself. 24.37.192.210 14:08, 17 September 2007 (UTC)

What the heck....sorry I`m newbie on this subject!

Is there suppose to be an equation to determine the wave function of a certain element using Radical Functions multiply Angular Function?PSI does it refers to the measurement or the Greek later to represent wave function?I understand that they put forth the 3-d equation that norm equals ONE but where`s the explanation saying the 3rd dimensional is on a plane with axis X, Y , Z format?Wave functions suppose to determine a certain electron density psi.Correct me if I`m wrong!!Thank you!

 For example:Ψ=radical function * angular function
             Ψ=R*Y
 Using a # orbital(7): Ψ7gZ(to the 4th power)= R7g*Y7gZ(4th power)
             Z:Effective nuclear change for orbital in atom(atomic #)
             r:radius=52.9pm(picometre terms)
             g:# of orbitals
             R=4лr²

-mintypooh

Confusing sentence

This sentence is really unclear - any suggestions? I think I know what the author was trying to say, but before I change it I'd like recommendations. "It is a function from a space that consists of the possible states of the system into the complex numbers." PhySusie (talk) 17:27, 19 November 2007 (UTC)

First sentence

A wave function is a mathematical tool used in quantum mechanics to describe any physical system.

I thought the state of a general quantum field could not be represented by a wave function. But a field represents a physical system... I believe the whole point in blackbody radiation is considering the electromagnetic field as a physical system. Plus in the case of a particle, you need two wave functions if the particle has a spin - although you can combine them in a single object. --67.68.88.200 (talk) 02:17, 22 December 2007 (UTC)

No, sentence is correct, including the case of fields.--Michael C. Price 08:07, 20 February 2008 (UTC)

Wrong; in quantum field theory the state of a system is not a wavefunction (an element of Hilbert space) but is a linear operation on hilbert space. Second Quantization uses the C*-algebra and not wavefunctions to represent a physical system. Wave functions have difficulty representing situations in which particles are created or destroyed. Agalmic (talk) 15:23, 29 June 2008 (UTC)

Not wrong;

• Are you claiming that many particle states cannot be represented as Fock states ?
• C*-algebra is just one approach; others are not precluded.
• Wavefunctions have no problems with particle creation/annihilation - see Fock state again.

--Michael C. Price 07:25, 30 June 2008 (UTC)

mathematics

Greeting to all,

I am not very good at math. Anything greater than 2+ 2 needs a calculator. Queation: Can the symbol for Phi, be written with the slash at an angle or does it need to be vertical? I am reading Poussin's Secret, this figure appears several times. —Preceding unsigned comment added by Namwireman (talk • contribs) 21:52, 19 September 2008 (UTC)

The Greek letter normally has a vertical bar, but in maths it is italicized, as all symbols for scalar variables usually are, so that the bar becomes slanted. Example: Φ (normal), Φ (italic). --A r m y 1 9 8 7 ! ! ! 22:19, 19 September 2008 (UTC)

Hi, I also have a question about the math. Wave functions as explained here and elsewhere use the L inner product, so I assume they're supposed to live in L(C). But the "continuous basis" in the article of delta functions centered at x for each x in R isn't actually a basis of L. L only has countable dimension, not to mention the delta function isn't really in the space since it has support on a set of measure zero. Is there a rigorous way to describe the position basis or something that I'm missing? Sorry, I've been trying to learn quantum and this has been bothering me. Rckrone (talk) 18:12, 22 June 2009 (UTC)

Mistake?

In the 1 particle in 3-dimensional -case, does that R belong to that formula which should be "integral taken over the whole space"? —Preceding unsigned comment added by 80.221.43.125 (talk) 03:13, 24 November 2009 (UTC)

Dives in too deep, too fast

I'm a sophomore in university, I do not have a Ph.D. in high energy physics. I would like to think I know a little more than the basics of physics and science in general, and I'm mathematically sound. However, this article dives straight in jargon that would only be understandable by post-grads, and the math is diving straight into multivariable calculus. Perhaps there's nothing you can do about the math, you can't simplify something that is this complex, but the explanations should at least be understandable by an educated person before delving into Ph.D. territory.

If it's just me, and other people find this article to be just fine, then nevermind I guess. —Preceding unsigned comment added by 62.178.103.91 (talk) 23:24, 6 January 2010 (UTC)

What is this Article Talking About?

i didn^t understand nothing from this article. it doesn't put a constitutive definition nor an operational definition of "the thing called wave function".

start with telling the reader "what this thing is"...???

and why it is called "wave"...???

is it a function like "f(x)=ax^2 + bx + c" ???

this article looks like a brain masturbation of a "Ph.D. in phsics" owner.

someone should re-write entire article starting with "what a wave function is" continuing with "what it is used for" then the meaning of "wave" word. should also put real life examples. —Preceding unsigned comment added by 78.162.148.204 (talk) 08:51, 9 June 2010 (UTC)

As far as I can make out the above is intended to be a request to have the article re-written to make it comprehensible to a layman without mathematical knowledge. I fully agree that, as far as possible, articles should be comprehensible to lay people. However, "wave function" is a highly mathematical concept, and I am not sure that it is possible to make it more accessible than the present article does. JamesBWatson (talk) 10:55, 9 June 2010 (UTC)

Merge into quantum state?

There is already a more general article on Quantum states. Why is there a separate one here about the wavefunction? This is especially absurd (and possibly, inadvertently, obscurantist) given that discussion of "wavefunctions" has been expanded to include discrete-basis state vectors. The two should just be merged into a single article on the quantum state or state vector.Bkalafut (talk) 10:57, 27 June 2010 (UTC)

About Definition of Countable Components Case

Is it right to say that vectors having countable basis is wave function? I think wave function usually refers to position-dependent functions. There is no such dependence on the definition of the article. --StarLight (talk) 21:24, 25 July 2010 (UTC)

Move lots of content to quantum state?

We have two very-overlapping articles: This one and quantum state. I propose that this article (wavefunction) should be restricted to discussions and definitions in the position basis (or position plus spin basis, or two-particle position-position-basis, etc.), and all the general discussions about linear algebra etc. should be cut-and-pasted into quantum state. Thoughts? :-) --Steve (talk) 17:57, 26 October 2010 (UTC)

I can't see any logical reason for such an arbitary division, which I'm sure would create confusion. --Michael C. Price 09:37, 2 November 2010 (UTC)

On second thought, momentum space stuff should probably be here too. I guess the scope of this article should be "pure quantum states represented as functions on the real line (or higher dimensional spaces)". --Steve (talk) 18:35, 26 October 2010 (UTC)

First sentence

I've been working on other quantum mechanics articles, and a casual reader coming from there to here to find out roughly what the term 'wavefunction' means needs an understandable definition in the beginning of the lead. Hence I've lengthened the first sentence to "A wave function or wavefunction is a mathematical tool used in quantum mechanics to describe the quantum state of a particle or system of particles." I hope this is okay, maybe it should say physical system or something rather than system of particles, as long as it's something that's meaningful to a layman. --Hermajesty21 (talk) 00:03, 26 December 2010 (UTC)

Diagrams for interpretation

The article really needs more diagrams relating mathematics to physics... the wavefunction can be visualized. I produced a couple for the wavefunction in one dimension and for one particle, hopefully it makes interpretation clear(er). Maschen (talk) 16:04, 23 August 2011 (UTC)

The positioning of the images need improvement, although I'm not sure how to do that. Good images, though. -- cheers, Michael C. Price 18:53, 23 August 2011 (UTC)

Thanks for feedback, but how do you propose to adjust the images? The page to image syntax is in the article Misplaced Pages:Picture tutorial. Maschen (talk) 23:31, 23 August 2011 (UTC)

Reforming the article

As can be seen above this article has had a lot of problems and a negative history (I know - I have complained just above), which shouldn't be the case for a topic like this. To set the article streight the following should be resolved.

1. A lot of mathematics is repeating thoughout the article in a way that doesn't help, especially on normalization, where there is an entire article on Normalizable wave functions, so there is repetition with another article as well. Some notation for probability is non-standard. It best to state space over which the wavefunction is defined and the probability integrals for finite volumes of space, since normalization is then just the integral over the full space, equal to 1. The normalzation condition only needs to be stated once. Also, first there was not eneogh explaination as to what wavefunctions are (in QM), now there are repetions of the vector formalism at the beggining then end of the article.

2. Also, since wavefunction spans a number of contexts shouldn't a disambiguation page be created? Before this is done, the current page should be moved to a new name titled Wavefunction (quantum mechanics), then the other applications of wavefunctions (such as PDE solutions as stated above) can be developed into new artciles. Then the disambiguation page can be created.

Maschen (talk) 10:03, 24 August 2011 (UTC)

Problems with recent edits

Here are a few of many problems I have with the recent edits to the article:

• "Note that the wavefunction describes a system of particles in a quantum state, it does not "describe the behaviour quantum state" itself, which is defined by quantum numbers." <-- I have no idea what this means
• "Simple examlpes of wave functions are common quantum mechanics problems; the particle in a box, which corresponds to wavefunctions for standing waves at various vibration modes, and the free particle (or a particle in an infinitley large box), correspoding to a wave function for a travelling wave (in this case sinusoidal)." <-- Even ignoring the typos, and the lack of clear explanation, this is wrong. The wave functions for a particle in a box are any continuously-differentiable function inside the box which is zero at the edges of the box. The stationary states are standing waves, not the wavefunctions. Likewise, the free particle wavefunctions are any normalizable continuously-differentiable function of space, not just traveling waves.
• "By the uncertainty principle, the momentum uncertainty is less than the position uncertainty (momentum is known to a higher degree of accuracy than position)." <-- Huh????
• "In all cases, the wave function provides a complete description of the associated physical system - it contains information about the system to be extracted by operators." <-- A typical reader will not understand the phrase "to be extracted by operators"
• "Note that ψ is not a function of any of the quantum numbers because they are not continuously variable, they are only integer parameters to label a specific wavefunction for a quantum state defined by the required quantum numbers." <-- You seem to misunderstand quantum numbers. It is perfectly possible to have an electron in, say, a superposition of 1s and 2s states in a hydrogen atom. The spatial quantum numbers are optional labels and do not need to be mentioned in the definition at all. The spin quantum numbers should be inside the parentheses, because ψ is a function of them. ψ is a function simultaneously of continuous spatial variables and discrete spin variables, and the normalization condition involves its integral over continuous variables AND sum over discrete variable.
• "A wave function is either a complex vector with finitely many components or countably infinitely many components." <-- Doesn't a free particle has uncountably infinitely many components??
• "The modern usage of the term wave function extends to a complex vector or function, i.e. an element in a complex Hilbert space." <-- A key point is that function can be viewed as a type of vector, because the set of all possible functions is an infinite-dimensional vector space. This might be the hardest and most important mathematical aspect of introductory quantum mechanics courses. This sentence not only fails to explain this, it doesn't even get it right. ("vector OR function"??)
• Hydrogen atom example:

• Again, this is an article about wavefunctions, not stationary states. This is written as if they were the same thing.
• Formula for the Bohr radius is incorrect by a factor of two, and should not be written in Gaussian units without saying so. People usually assume SI.
• What is the reader supposed to learn about wavefunctions by reading this example? I can't think of anything. They'll just see some formulas, but have no idea why the formulas are true or what the formulas mean or why they should even care.

• "Below the basis vectors are unit vectors, which are completley arbitary but non-equal, non-zero, and dimensionless." <-- This is wrong. You can't pick three vectors all in the same plane and expect them to be a basis for position space. Everything in this section is so much more complicated by the decision to include both rectangular and polar and cylindrical coordinates all at once. Why make things so complicated?? Why not just use x,y,z?? With statements like "and X is some dimensionless factor, possibly dependant on any of the coordinates ${\displaystyle \scriptstyle {r_{1},r_{2},r_{3}}\,\!}$", only very mind-reading readers will understand that this is referring to the "sin θ" factors of polar-coordinate integrations and so on. The mechanics of doing integrals in spherical and other coordinates is the subject of other articles on wikipedia; for this physics article, we can just write the integral in normal notation.

Well that's just a few to start. I wish people would not edit extensively articles on subjects they don't understand very well. :-( --Steve (talk) 15:04, 28 August 2011 (UTC)

The next worse things are the diagrams I added - arn't they ?...

This isn't a vain self-obsessed attempt to add material to an article so my name takes up the edit history (i'm not in for credit), I actually want to help draw images relating maths to physics as (if only slightly) clearly as possible. More were planned for three dimensions and multiple particles but when I try fixing up maths it always ends up over-complicated, so the diagrams will lead to the wrong ideas...

I should add though about the quantum numbers, that in the definition section the numbers n₁, n₂ etc are any quantum numbers, no specific one is the principle, spatial or the spin quantum number. The n is misleading.

Maschen (talk) 23:51, 28 August 2011 (UTC)

About motivations: I have no doubt that you have been working hard and altruistically, don't get me wrong :-)

About quantum numbers: In a math course, you might define a function ${\displaystyle f_{1}(x)=5x+11}$ and another function ${\displaystyle f_{2}(x)=16x-12}$. The "1" and "2" are just labels. The teacher would say "These are examples of linear functions. In general a linear function would be ${\displaystyle f(x)=ax+b}$". The teacher would not say "In general a linear function would be ${\displaystyle f_{i}(x)=ax+b}$ where i is the number that labels the function." The quantum numbers are the same sort of thing, they are just labels. For example, the 100 orbital of the hydrogen atom is the function ${\displaystyle \psi (r,\theta ,\phi )=e^{-r/a}}$. Some people might choose to use ${\displaystyle \psi _{100}}$ as the label for this particular ${\displaystyle \psi }$. Other people might just call it ${\displaystyle \psi }$, as in "Let ${\displaystyle \psi }$ be the 1s wavefunction of a hydrogen-atom electron...". Or they might call it ${\displaystyle \psi '}$ if they previously used the letter ${\displaystyle \psi }$ for something else. Or they might use a different letter, ${\displaystyle \phi }$. Anyway, the spatial quantum numbers are just labels. They do not belong in the general abstract definition. In the general definition you can use ${\displaystyle \psi }$ with no subscripts, and people will understand that it's also OK to give wavefunctions other variable names, like ${\displaystyle \psi _{100}}$ or ${\displaystyle \phi }$ or whatever. I'm mainly talking about spatial quantum numbers but this is true for spin too: Spin belongs as an argument inside the parentheses, along with the coordinates, not as a subscript. There should be no subscripts in the general definition.

About diagrams: I like them, but I'm not sure they all belong in this article, because wavefunctions are not the same thing as stationary states. It seems to me that the solutions to the time-independent Schrodinger equation are part of the topic Schrodinger equation and stationary state but not really an important part of the topic of wavefunction. The wavefunction is the mathematical apparatus that is used for describing any state, whether or not that state happens to be an energy eigenstate. Of course it should be mentioned in the article that a wavefunction might be a stationary state, and some examples can be given of wavefunctions that happen to be stationary states, but the properties of stationary states should not be the dominant theme of this article, and examples of stationary states should certainly not be the only examples of wavefunctions in the article. There should be non-stationary-state examples too so that readers don't get the wrong idea that wavefunction is another word for stationary state. In my own illustrations of wavefunctions ( ), you'll see that I have always put both stationary and non-stationary states for exactly that reason. :-) --Steve (talk) 03:54, 29 August 2011 (UTC)

Ok - thanks for constructive feedback, as always. So some next changes to make are then:

1. Remove subscripts in definition (and explanatory context related to them), insert the spin number s since its the fundamental property of the particle/s, which would appear as

${\displaystyle \psi =\psi \left(\mathbf {r} _{1},\mathbf {r} _{2}\cdots \mathbf {r} _{N},\mathbf {S} _{1},\mathbf {S} _{2}\cdots \mathbf {S} _{N},t\right)\,\!}$

linking to spin (physics) article and possibly stating

"where

${\displaystyle S={\sqrt {s\left(s+1\right)}}\hbar ,\quad s=n/2,\quad n\in \mathbf {N} \,\!}$

and N = field of natural numbers".

2. The curvature image doesn't really belong to the article I suppose. Either eliminate or move the curvature images to the Schrödinger equation article, to the Versions,Time-independent equation section where the wavefunction is described in 1 dimension and is time-independant.

The other images are not just standing waves as stationary states though, there are travelling wavepackets. There's nothing exactly wrong with that since as you pointed out ψ can be any continuously differentiable functions, and travelling waves are just a specail case. As I said more images were planned; for stationary and non-stationary states, so if I was to add more stationary-only states wouldn't become the theme.

Also isn't continuously differentiable one criterion for a function to be continuous? Continuity was stated in the Born interpretation section.

Maschen (talk) 07:59, 29 August 2011 (UTC)

About spin: You do not understand how to incorporate spin into a wavefunction. Therefore I suggest that you don't write about it! (This is true for other topics too! Do not write about things you don't understand well! Please please please!!) You can just give the definition for spin-0 particles, which you seem to at least slightly understand. Maybe someone else will incorporate spin later. This is the approach in most introductory textbooks anyway: Usually only spin-0 is discussed in the first introduction.

About the Schrodinger equation article: The article right now is a general discussion of the fundamentals of this broad and important topic. It doesn't get bogged down in details like "How can I solve the 1-dimensional time-independent Schrodinger equation in my head?" I do not suggest that you edit the article to bog it down with these details! I suggest you leave it alone. :-/ --Steve (talk) 13:16, 29 August 2011 (UTC)

Fair enough - I’ll just delete my curvature image, the subscripts in the definition and not touch anything after...

Before I zip it and leave you all in physics/maths tranquility: I didn't say it before either - i've seen your images before you linked to them, they were better than mine since they were animations including real and complex parts of the wavefunction.

Maschen (talk) 17:06, 29 August 2011 (UTC)

That's very kind of you to say! I had a go at rewriting, you are more than welcome to complain if I deleted something useful and good, or wrote something bad, or whatever. Maybe it was accidental, or maybe I had a reason and I can explain and discuss. --Steve (talk) 19:46, 3 September 2011 (UTC)

Not at all. Most of you here seem to be postgraduates, post-doctarates or beyond, so I respect your positions, and it must be a P ! A ! I ! N ! to have early undergraduates (only just about to start 2nd year) get this all wrong... many of you would be better at writing this topic than me.

The only slight objection is; (I know its only notation), but why use subscripts instead of brackets for the probability notation? Perhaps its easier to read? And for "all space" in the integrals why not give a symbol - at the top of my head why not \mathcal{R} (caligraphic R), to take repetition of words out and for ease of writing? Well it doesn't really matter anyway...

When I first came to the article I never intended to touch any of the maths and only meant to add diagrams, but the probability formalism seemed (to me at least) a little ropey so I found myself re-writing half the article wherever probability came in, and over-generalized. Sheesh its guilt to leave all the work to postgrads or beyond to tidy up the mess, I really need to use talk pages BEFORE editing anything...

Maschen (talk) 21:35, 3 September 2011 (UTC)

No worries. :-) About subscripts: I dunno, that's the way it was last month. I guess parentheses can be functions or multiplication, whereas a letter with a subscript is expected to be just a number, which is what it is. Other notations are also OK, don't get me wrong. About "all space", I was trying to minimize the amount of time it takes for an average reader to take in the equation. But I know it's non-standard. I think ${\displaystyle \mathbb {R} }$ is the most common symbol for 1-dimension, or ${\displaystyle \mathbb {R} ^{n}}$ for n dimensions. I'll put that in... --Steve (talk) 02:32, 4 September 2011 (UTC)

Awesome! Thats tons of hard work you've done, i'll reward you when I find out how. Cheers - Maschen (talk) 10:07, 4 September 2011 (UTC)

Hydrogen Density Plots

It might be an idea to make the image File:Hydrogen Density Plots.png bigger to about 450 × 450 px? so the quantum numbers can be seen while reading the article instead of having to click on it each time. Thats how it is in the Quantum state article. Maschen (talk) 10:34, 4 September 2011 (UTC)

I thought I would just do it, clearing any odd spelling typos while at it - this much editing will not harm. Maschen (talk) 10:34, 4 September 2011 (UTC)

Ontology of the Wave Function needs its own article.

It's an incredibly interesting subject with major thinkers struggling to find answers for it and we only have a petty paragraph. Also it can not be claimed that not a lot can be written because that small paragraph cites several big thinkers who have public texts. --62.1.29.164 (talk) 12:59, 4 September 2011 (UTC)

A number of articles seem to be possible from the term Wavefunction. If a new article on this is to be written it will need

its own name - presumably and without shock Wavefunction (ontology). Then this article may need to be called something else more specific, related to the wavefunction in QM. On top is are the issues above for other applications of wavefunction, which may have their own names. I did move the page at one time from Wavefunction to Wavefunction (quantum mechanics) but an admin moved it back. Thoughts on creating a disambiguation page assocaited with the term wavefunction and all the names of the articles need to be considered before creating the new article, and to be sure they don't mutually overlap too much with each other or with other QM articles.

I don't suppose that helps much, chances are you knew this already... Maschen (talk) 21:03, 4 September 2011 (UTC)

The ontology of the wave function already has its own article. The article is: Interpretations of quantum mechanics. I just added better links so that readers will not miss it. :-) --Steve (talk) 19:10, 5 September 2011 (UTC)

Ok, never mind I guess... Maschen (talk) 00:06, 6 September 2011 (UTC)

Diagrams again...

All this time didn't even add spin-0 particles for the 1d 1 particle diagrams, as should be months ago...

Maschen (talk) 15:56, 9 October 2011 (UTC)

Clarifying abstract and real qualities

Removed to talk page for discussion per WP:BRD (bold, revert, discuss cycle). Nvallejo, the reason given in your edit summary, Reinstated correct science unjustly removed (do the science please don't promote theories), should be based on WP policy and guidelines, not on your professional opinion. Your contribution appears to exclude some interpretations of quantum mechanics. Please see the policy on WP:NPOV (neutral point of view). Thanks and welcome to WP.—Machine Elf  14:38, 14 October 2011 (UTC)

There is much misinformation and confusion with regard to wave functions and their physical significance when in fact there should not be. The student is advised to understand the distinction between what can and cannot be measured in the laboratory to avoid adding fallacious properties to quantum entities. The wave function of a fundamental particle is a complex quantity and should never be associated with a physical reality. Max Born won his Noble Prize for showing that the position at any instant in time for an entity (particle) obeys a probability distribution and therefore the particle’s position changes instance to instance probabilistically. No wave function has ever been measured and the fact that they are complex quantities associates them with something that is not physical. This is a restriction that is formally placed upon the development of the Schrödinger equation that relates a first time derivative to a second space derivative causing the solution of the differential equation to become complex. Wave functions have no physical significance. They reside in complex phase space. They are templates for where you may find the particle. At their wave crests and troughs, you have a high probability of finding them in any measurement, but that is all. Probability is a law; it is subjective and cannot be “found” like a piece of spaghetti. Raymer and Smith point out:

“A wave function of a single object represents the quantum state of that object, and is not measurable, even in principle.”

Eisberg and Resnick point out: "The fact that wave functions are complex functions should not be considered a weak point of the quantum mechanical theory. Actually, it is a desirable feature because it makes it immediately apparent that we should not attempt to give to wave functions a physical existence in the same sense that water waves have a physical existence. The reason is that a complex quantity cannot be measured by any actual physical instrument. The 'real' world (using the term in its nonmathematical sense) is the world of 'real' quantities (using the term in its mathematical sense)."

The complex mathematical representation arises because the position of the particle is not directly coupled at any one point in time and space to an absolute reality, hence it cannot be equated with that which we regard as real. The particle requires a mandatory manifestation time before it becomes a defined entity over a region of space. Any attempt to violate that will result in unrealistic errors that destroy its time / space integrity as pointed out by Heisenberg’s Uncertainty Principle. Remember Schrödinger’s equation is developed, not derived, however it has never been violated in experiment. In the early development of Quantum Physics, there was no reasonable way to reconcile the abstract properties of particles with their real (objective) time / space co-ordinates and therefore Schrödinger developed a plausibility argument for constructing a wave function. Initially, Schrödinger assigned the charge distribution of a particle to its wave function. That was later shown to be inaccurate by Born. The mathematical reason that one must develop rather than derive the equation is because there is no objective measurable quantity that one can find in the real world to support their existence as real entities. Had that not been the case, the wave associated with the particle would have immediately yielded a valid physical existence. We find however, that the only useful information regarding a wave equation is the probability amplitude which is basically a magnitude. It tells us the magnitude of the probability of finding the particle at any point within its manifestation region.

Problems with attaching a physical significance to wave functions

"The Ether (Aether)" was an attempt to formalise a physical but hidden medium for the transmission of particles and energy. It was a failed attempt because one still needed to physically verify the existence of something in order those entities be related in real time / space to account for their movement and existence. What complex wave functions do therefore is tell us that the particle is related to a higher dimensional reality, not a physical one.

Real world analogies

Wave functions are analogous to aircraft flight plans. There is no objective plan to speak of, only the concept in the mind of the pilot or flight controllers. Yes there may be a plan on paper, or a space region over which the craft will travel, but there is no physical significance whatsoever to it. The only physical entity is the aircraft itself. Another example is that of an empty football stadium and a spectator. Born’s postulate tells us that at a time instance, we may find the person at any seating position and the wave function tells us how large the probability is concerning finding the person at different areas of the stadium. Subsequent measurements will reveal the person to be in any position allowable concerning that. This tells us that the person may be for instance on one side of the stadium in one measurement, and then at a diametric position in the next. Concerning an electron orbiting its parent nucleus for instance, it is not obliged to follow an ordered traversal of its orbital. It is a higher dimensional entity, not physical. Heisenberg’s Uncertainty Principle tells us that to be physical, we must only measure the person outside of the stadium, so our accuracy, is restricted to a person being the size of the stadium. The particle is therefore transiting higher dimensional reality instance to instance as the flashes of cameras at night in that stadium full of people would appear and disappear. Wave functions to this day remain abstract.

Excuse me?

With regard to remaining unbiased and having a "neutral view", you should first understand the science of exactly what you are talking about and it appears as though you know nothing with regard to that. This page itself shows blatant mathematics already submitted that is supporting my science and the work of Nobel laureates of the past. Complex functions are not real functions and the entire page details the existence of these waves as abstract only. They form a complex vector space:

• Schrödinger’s wave equation is complex
• Max Born won his Nobel Prize for showing that fundamental particles obey a probabilistic wave function
• I have provided references to text and papers that support the science that these wave functions are not real
• There has been no scientific effort that has ever shown the contrary
• Wave functions being unreal (complex) is science
• Wave functions being real then, reside in the realm of speculation and theory only and should be classified as interpretation

Please leave your comments for somewhere else associated with interpretation and do not remove legitimate science unless you are able to show that wave functions are real. My addition shows science only, your views are not neutral and remain biased. There cannot be two interpretations from one set of science. The entirety of literature associated with this topic (not its interpretations or theories), has shown only abstract qualities of the entities in question. Your comments are therefore unwarranted and cannot stand up to any scientific scrutiny whatsoever.

So please refrain from removing the addition again, unless of course you have science that says the opposite.

Nvallejo (talk) 04:05, 15 October 2011 (UTC)

I've removed it now. I don't really care about the science of it one way or the other. The section you added was completely unencyclopedic in tone. We don't "remind the student" of anything. This is an encyclopedia. Not a textbook. I'll leave it to others to argue the scientific merits of your addition once the tone is cleaned up. As a general note, if someone reverts you and points to the talkpage, please don't reinsert until a consensus has been reached. Thanks! Sperril (talk) 04:17, 15 October 2011 (UTC)

No problems ! I made no attempt to assume that the format of the addition was in any way perfect. This addition has been deleted from the outset and not allowed in any size shape or form to be adjusted or corrected. These people are not approaching the site or its participants with the correct respect they deserve. If this is to be discussed upon its scientific merit and altered to reflect necessary changes, then I have no problem whatsoever in engaging people in useful debate. I will not tolerate 'roaming patrols' on this site deleting at will subject matter that 'they deem' inappropriate. This is how I would have welcomed someone:

'Dear Sir, thanks for your addition to the subject in question. It appears that you have pointed out some relevant points of science concerning Wave functions however the format is in need of attention. Please go to the talk section of this page and we will endeavor to rectify it.'

No such help was ever offered. Nvallejo (talk) 04:38, 15 October 2011 (UTC)

Hi Nvallejo, and once again, welcome to Misplaced Pages. In fact, you've been offered a good deal of help. The clickable links that start with WP, like WP:BRD and WP:NPOV, are links to policies and guidelines that you should read as soon as you get a chance. As I said above, Talk:Wave function#Clarifying abstract and real qualities, your contribution was moved to the talk page for discussion per WP:BRD (bold, revert, discuss cycle). The reasons you gave in your edit summaries:

1. Reinstated correct science unjustly removed (do the science please don't promote theories),
2. Reinstating correct science. (There has been no consultation here with the author of this revision. Let that be noted.),
3. You are conducting consistent unwarranted removal of correct scientific literature.
4. Unencyclopaedic tone corrected. Arbitration is the next step given blind reversion is occurring with no discussion.

are not appropriate, they should be based on WP policy and guidelines, not “your science”. I'm certainly not be a “Nobel laureate”, but I can tell you're not one either. Two other editors have reverted your contribution as well, and while I'm glad to see that you've eventually engaged on the article's talk page, please keep our policies on WP:CIVILITY and WP:NPA (no personal attacks) in mind when communicating with other editors in the future.

You are the one who has treated others disrespectfully here, and you have introduced yourself in very bad light with comments like:

• “I will not tolerate 'roaming patrols' on this site deleting at will subject matter that 'they deem' inappropriate.”

I expect you address the WP:NPOV concerns respectfully Nvallejo. Please be advised that you must not to revert a fifth time, (see WP:3RR). I'll leave a template with more information on your talk page. Please don't take offense. It would however be wise not to avail yourself of the warning templates until you know what you're doing, (I was not editing disruptively, see WP:DISRUPT).—Machine Elf  16:16, 15 October 2011 (UTC)

I've included the fourth edit summary… I hope you stick around long enough to learn just how silly it was.—Machine Elf  16:45, 15 October 2011 (UTC)

Where's the discussion?

You pull my material off the page, and now no discussion?
Ok, here's what I want:

• Provide reference to a scientific text (preferably one being routinely used in teaching the subject world wide today) that shows wave functions are real, both in a measurable and mathematical sense of the word (no references to interpretational or theoretical texts allowed)
• Explain why you are insisting wave functions are anything other than unreal considering the page in question is already composed of Complex Mathematics
• Formally refute the references that I have given concerning wave functions being cited as entirely unreal and unable to be proven as being anything other, these being scientific texts, not theoretical.
  

Lets resolve this quickly.

Nvallejo (talk) 08:20, 16 October 2011 (UTC)

How high. I've moved the latest WP:IDHT here from my talk page where I've brought WP:V, WP:SYN and WP:OR to Nvallejo's attention. Let's keep it here with the rest of the alphabet from now on, k, thx—Machine Elf  09:45, 16 October 2011 (UTC)

Ok, I know it sounds like I'm the bad guy here however your initial three editors amount to only you and your friend. The other editor made reference quite congenially to the format of the addition that I made and I obliged that person due to their helpful nature. Neither yourself or MCP have expressed any of the same helpful advice or information.

With regard to the PWF paper, it states categorically that one is unable to measure a single photon WF and must use an ensemble method in order any physical attribute become evident.

The Eisberg Resnick disclaimer makes no reference to the wave function having a physical existence! they only talk about physical interest so what? No one is arguing the particle is a real entity. The wave function is the unreal aspect and is only a template for its position. It has thus far been unable to be described in real terms by anybody.
So you have still failed to provide any mathematical real representation of what it is we are talking about? All of the mathematics in PWF is complex as is any other reference you choose to name, including the WP page itself! I mean what are we really arguing here?

Yes the wave function will contain all of the information for the existence of the particle only if we measure it outside of a general region of locality. Any attempt to measure inside that translates our calculations to the complex plane. For a measurement to be regarded as real, that measurement may only occur outside of the manifestation region (wave packet) of the particle as it transits physical reality in Planck Time units.

Regarding the particle transiting position to position, the particle itself does not possess an initial state. Experiment today in quantum entanglement indicates the particle is in higher dimensional reality until it is measured and thus conservation of particle state occurs faster than light. Distance appears to make no difference if entangled particles are measured at the same time across vast distances.

Eisberg and Resnick p135 restate Born’s postulate as does the WP page;

If, at the instant t, a measurement is made to locate the particle associated with the wave function Ψ(x,t), then the probability P(x,t)dx that the particle will be found as a coordinate between x and x + dx is equal to Ψ*(x,t)dx Ψ(x,t)dx

Note: dx may not go to zero.

This indicates that the particle’s position is probabilistic only in any given time instance t1 meaning that if we measure it and obtain its exact position inside of its wave packet then Heisenberg’s Uncertainty Principle says we may do so but that we must also obtain a corresponding unreal value for its complementary aspect in the measurement i.e. its velocity/momentum. Now, if we then perform another measurement at t1 + dt the precise instance after the last (considering there must be a definite unit of time between these instances) then we may be assured that the particle will be at any probabilistic position inside of its manifestation region yet again. The particle is not obliged to follow an ordered traversal to its next position. That is exactly what Born's postulate says.

In the case of an electron for instance orbiting a nucleus, the 3D wave function (orbital) allows the particle to appear instance to instance at any of the allowable positions inside of that wave function i.e. it can be in one instance on one side of the nucleus and then at another instance on the other side. This is how Quantum Tunnelling occurs when a particle “penetrates” a potential barrier of greater energetic height than the particle itself. Tunnelling only occurs because of this position equation as detailed by Born. Classical physics cannot resolve it as uniform trajectory. We also note the electron cannot go through the potential barrier of the nucleus so must always navigate around it.

The physical significance then of any wave function is only that it dictates where the particle is, not that the particle is it.

Photons act differently because they are transactions. You cannot localise a photon, it will be transformed immediately. Photons are energy transactions between particles that have state i.e. as soon as a photon is localised, it is destroyed, however that is only an interpretation because you cannot destroy energy. The localising mechanism, absorbs the photon's energy. The PWF paper therefore discusses only the wave aspects, and details that one cannot associate a photon with a particle as such. They have no mass and no position eigenstate.

Again, I cannot see in any of what you have cited, fair comment that there is a real mathematical interpretation for WF's? Can anybody show me some evidence please, anything?

A reference to a text (non-interpretational or theoretical) or paper? Cite something and reproduce it please.
Given MCP was also involved in deleting my work, perhaps he would oblige in discussing this now?
Kind Regards to all involved in this discussion.

Nvallejo (talk) 10:45, 16 October 2011 (UTC)

Nvallejo, I don't know whether you don't understand the interpretative issues, or whether you choose purposely to ignore them as a debating tactic; either way, further discussion is pointless until you take on board what others say. The ontology section says all there is to say on the matter, with links to where the issue is dealt with in more detail. -- cheers, Michael C. Price 11:48, 16 October 2011 (UTC)

I can't see how you can possibly ignore what is taught to people in their first year of physics? All of the interpretations that you are referring to assume the wave function as real! The science from 1926-27 is where it all happened and further from there has only ever been these interpretations i.e. real wave functions. None of them have ever become the science of wave functions themselves. It would be different (and I would be able to see your point) if the science and mathematics was real and the interpretations were not...the case is quite the opposite as detailed in the interpretation of quantum mechanics page.
By owning this site, you and whoever else is telling people that wave functions are like water waves in the opening of the page is a travesty. It is misinformation. As I keep pointing out, the WP page itself and all of the mathematics is abstract! How can someone like myself come to any other conclusion that you are deliberately trying to conceal the abstract nature of these waves because what is in front of unsuspecting people is exactly that, and you do not wish them to understand that. You cannot possibly be a teacher! or an objective scientist.
My intuition tells me this. You have a bias toward making sure that the universe remains entirely enclosed in a single dimension and explainable as such because you are involved in the development of theory that points out exactly that. So you own this site with your friends to make sure that others don't arrive at the correct understanding and are forced into the realm of speculation. I would imagine that other people have come across the same problem with you guys and that is disgraceful given you are leading people down an incorrect path, especially students. This site has a bad name because of people who can pervert the truth and my experience here is reaffirming that. There has been no concrete evidence forwarded by you in any size, shape or form. It's always, 'go somewhere else' or some damn excuse to avoid discussion.
The evidence is right in front of anyone who wants to look at it. Your attempts to make my summary of the science appear an interpretation amount to your efforts to control the page and the information. Unless you can come up with alternative science and mathematics that shows wave functions to be anything other than unreal, I see no reason as to why that addition should not be left on the page.
Nvallejo (talk) 06:33, 17 October 2011 (UTC)

WP is about WP:NPOV, which means all significant POVs are presented, as in the Ontology section and over at interpretation of quantum mechanics (where the wf is not assumed to be real, despite your claims to the contrary. And BTW abstract does not mean unreal.) -- cheers, Michael C. Price 06:46, 17 October 2011 (UTC)

Formalism section?

The formalism section now seems redundant, since much of the vector formalism there has been incorperated into the wavefunctions in vector form section. Though I would rather not delete the formalism section, since its someone else's work and there are some extra bits which may be of use. I'll leave it to anyone to decide for now... F=q(E+v^B) (talk) 22:31, 15 October 2011 (UTC) — Preceding unsigned comment added by F=q(E+v^B) (talk • contribs)

1. Robert Eisberg, Robert Resnick (1985). Quantum Physics of Atoms, Molecules, Solids, Nuclei, and Particles - Second Edition, p. 135. John Wiley and Sons. ISBN 0-471-87373-X.
2. Brian J. Smith, M G. Raymer "Photon wave functions, wave-packet quantisation of light and Coherence Theory", P. 18 New Journal of Physics
3. Robert Eisberg, Robert Resnick (1985). Quantum Physics of Atoms, Molecules, Solids, Nuclei, and Particles - Second Edition, p. 134. John Wiley and Sons. ISBN 0-471-87373-X.

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