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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)

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