Talk:Wavefunction

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[edit] 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 [1] 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.


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

[edit] 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 |1\rangle and |2\rangle. If the allowed states formed a vector space, then |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 ([2]) 26. Mar 2006 16.55 (CET)

[edit] constraints

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

[edit] 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. e^{i\Theta(\vec x)} \Psi is physically the same as Ψ (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)

[edit] No meaning

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

[edit] 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 Parkhurst 23:00, 01 November 2006 (KU)
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)
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