Talk:Wave function/Archive 2

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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^(talk) 00:12, 21 February 2007 (UTC)

Ok, that's done, and Normalisable wave function as well. Cheers. -GTBacchus^(talk) 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 ^talk 23:50, 4 November 2007 (UTC)

I am glad you moved it. No less an authority as the on-line OED redirects wavefunction to wave function. For those of us who poo-poo "authority" let's at least follow the logic of grammar and present day English usage. Wavefunction would be following the germanic eigenfunktion where one can join two nouns and keep them in equal importance. In English wavefunction would mean that wave is a prefix and function is the root. Prefixes are meant to modify or adjust the stem (according to the OED), much as adjectives do to nouns. A wavefunction would be akin to a wavy function, I suppose. Using one noun to modify another noun usually has a genetive meaning. Thus "wave function" is akin to a "function of a wave", mathematical I suppose. It gets trickier with the ablative meaning in the OED's example "speedboat ride", "ride on a speedboat". Laburke (talk) 03:05, 30 October 2011 (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 ^talk 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 Wikipedia: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 $\scriptstyle {r_{1},r_{2},r_{3}}\,\!$", 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 $f_{1}(x)=5x+11$ and another function $f_{2}(x)=16x-12$. The "1" and "2" are just labels. The teacher would say "These are examples of linear functions. In general a linear function would be $f(x)=ax+b$". The teacher would not say "In general a linear function would be $f_{i}(x)=ax+b$ 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 $\psi (r,\theta ,\phi )=e^{-r/a}$. Some people might choose to use $\psi _{100}$ as the label for this particular $\psi$. Other people might just call it $\psi$, as in "Let $\psi$ be the 1s wavefunction of a hydrogen-atom electron...". Or they might call it $\psi '$ if they previously used the letter $\psi$ for something else. Or they might use a different letter, $\phi$. Anyway, the spatial quantum numbers are just labels. They do not belong in the general abstract definition. In the general definition you can use $\psi$ with no subscripts, and people will understand that it's also OK to give wavefunctions other variable names, like $\psi _{100}$ or $\phi$ 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 ([1] [2] [3]), 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

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

linking to spin (physics) article and possibly stating

"where

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

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 $\mathbb {R}$ is the most common symbol for 1-dimension, or $\mathbb {R} ^{n}$ 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 px²? 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)

Forget it... Maschen (talk) 00:06, 6 September 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)

Diagrams again...

I have returned for a while, having read up more about wavefunctions. I will not write content, but re-incarnate some diagrams from months ago...

Maschen (talk) 22:30, 26 October 2011 (UTC)

For the last diagram it might be worth adding to the caption that the two particles recoil off each other with 100% certainty, or words to that effect. -- cheers, Michael C. Price ^talk 06:44, 30 October 2011 (UTC)

Thanks, first feedback already positve, i'll add the caption and lauch the diagrams onto the main article. If someone dislikes then they'll delete - and (should) explain here... Maschen (talk) 01:54, 2 November 2011 (UTC)

I deleted the images there.. they in the article now and have stood the test of time in not being deleted, so I take it people think theyr'e fine.

Maschen (talk) 16:33, 21 November 2011 (UTC)

Historical context

Hi...

All: I added a brief (and rather vague even after all that time and energy...) historical outline of the introduction of the wavefunction in the 1920-30s, named all those physicists responsible and dated events, added referances. Furthermore added extra context in the definitions and re-headed the section, and tweaked a other few bits and pieces. Hope its better...

Sbyrnes321: Looking back through the edit history makes me realize you wrote the historical note (and much of the 1st 1/2 of the article) so I do apologize for that. I know its very l8 to say that now after the elaped time of a couple of weeks. Do you think this history expansion is fine? or anything on the article for that matter......

...all comments are very welcome...and feel free to complain about mistakes...

F=q(E+v^B) (talk) 02:42, 21 November 2011 (UTC)

Not at all, as far as I can tell. Maschen (talk) 16:33, 21 November 2011 (UTC)

Further modifications

• Re-wrote a few bits here and there so those sentences/phrases make sense.
• Re-grouped all the introductory stuff together, so that the formalism follows after. It still doesn't seem coherent enough.
  • All mathematical intro stuff has been placed under a new heading Mathematical introduction - so that a layman will know what's coming before rather than after.
• Re-titled the section Wavefunctions in vector form to Wavefunctions as vector spaces and removed the dablink:

" "Wavefunctions in vector form" are not and must never be confused with "Wave vectors", a different physical quantity and concept.",

- there is no need if the title it worded properly.

• I don't really know why I added the headings to the history section. They don't add anything so i'll remove them. This is a setion which should be written in continuous prose, not chopped into subsections.
• Also added more referances

On this page I mainly talk to myself, but indicated the reason for change anyway. --F=q(E+v^B) (talk) 14:55, 11 December 2011 (UTC)

The linear algebra has become very intricate and technical - but nessersary. None of it should be deleted, but its making the article very long. Since most readers will probably read through the introductory stuff, then look further down the page for more info, the show/hide table code can be used so readers not interested in the maths can skip it and carry on (or click "hide" if it too blinding), interested readers can click "show" and read on. Also the article will reduce in length so the scroll bar is not so awkward to use. It would propose its reasonable to add show/hide table code for each subsection of mathematical detial the linear alg. formalism. It'll also frame the maths and make it look better (perhaps).

-- F = q(E + v × B) 12:05, 15 December 2011 (UTC)

I reverted the last change becuase it was pointless. Its better to expose maths so its clearer what the subsections are about, then let readers click hide when it gets too much for them. --Maschen (talk) 16:54, 15 December 2011 (UTC)

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