Talk:Wave function

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Normalized, or not?[edit]

It seems, position-space and momentum-space wave functions are normalized, but others are not; and every linear combination of wave functions is a wave function... a mess? Boris Tsirelson (talk) 14:26, 30 April 2016 (UTC)

It says in the inner product section when a wave function is normalized, orthogonal, orthonormal, or not. MŜc2ħεИτlk 14:30, 30 April 2016 (UTC)
Yes, and still... even in that section, the interpretation of the inner product is given before introducing normalization. Does this interpretation of the inner product apply to non-normalized wave functions? Boris Tsirelson (talk) 15:45, 30 April 2016 (UTC)
"...this general requirement a wave function must satisfy is called the normalization condition..." So, really, must satisfy? Throughout the article? Or, depending on the context, sometimes? How does the reader know, when it must? Boris Tsirelson (talk) 15:49, 30 April 2016 (UTC)
Where does the article say "this general requirement a wave function must satisfy is called the normalization condition...". I can't find it anywhere. I thought the wave function must be normalizable for the probability interpretation to work, and collapse assumes normalized wave functions because the formula given is for the transition probability. MŜc2ħεИτlk 16:26, 30 April 2016 (UTC)
The lead, the paragraph before the last:
In Born's statistical interpretation,[8][9][10] the squared modulus of the wave function, | ψ |2, is a real number interpreted as the probability density of measuring a particle's being detected at a given place, or having a given momentum, at a given time, and possibly having definite values for discrete degrees of freedom. The integral of this quantity, over all the system's degrees of freedom, must be 1 in accordance with the probability interpretation, this general requirement a wave function must satisfy is called the normalization condition. Since the wave function is complex valued, only its relative phase and relative magnitude can be measured. Its value does not in isolation tell anything about the magnitudes or directions of measurable observables; one has to apply quantum operators, whose eigenvalues correspond to sets of possible results of measurements, to the wave function ψ and calculate the statistical distributions for measurable quantities.
Boris Tsirelson (talk) 16:47, 30 April 2016 (UTC)
The problem is, that the article is for now the mix of statements that are true when "wave function" means "normalized" (and wrong otherwise), and statements that are true when "wave function" means "not just normalized" (and wrong otherwise). Boris Tsirelson (talk) 16:51, 30 April 2016 (UTC)
Ack, careless me, missed the lead. Just tried rearranging more sections in the article to make the flow easier to follow. It would be helpful to separate off all content on the probability interpretations in its own section, and maybe rearrange statements when normalization is necessary and unnecessary. Maybe you would like to try? MŜc2ħεИτlk 17:10, 30 April 2016 (UTC)
Hmmm... let us think. The lead uses the probability interpretation, and this is necessary, since otherwise it is just some math. First of all, a wave function describes a quantum state, and here it must be normalized. But later, probably, it appears that physicists do a lot of calculations, postponing interpretation (till the end of calculation); and in this process they are, somehow, temporary, effectively, mathematicians... and tolerate non-normalized, and even non-normalizable, functions... and do not hesitate to call them wave functions... right? A kind of abuse of language. Surely, the superposition principle does not mean that a linear combination of wave functions is a wave function even if it is identically zero (which really could happen)! But, who cares... Really, not many centuries ago, mathematicians got true equalities after hard calculations with divergent series, without bothering too much... These intermediate divergent series were probably called "functions", but they were not...
But no, I am reluctant to edit physical articles myself. Since my text smells of math, inevitably, I know. And another, no less important reason: I never read elementary textbooks on physics, and so, I do not know, in which form all that is written there. Boris Tsirelson (talk) 17:58, 30 April 2016 (UTC)
The observation
...physicists do a lot of calculations, postponing interpretation (till the end of calculation); and in this process they are, somehow, temporary, effectively, mathematicians... and tolerate non-normalized, and even non-normalizable, functions...
is absolutely correct. This does not provide an excuse for us to do the same in this article, at least not before we tell the reader what is about to happen. I'll try to do my bit in due time. YohanN7 (talk) 16:43, 2 May 2016 (UTC)
Well, we must follow the physics that stretches outside Wikipedia... that is, "do the same"; but indeed, we should tell the reader what is about to happen. At least, it is done this way in math; for instance, "Baire set". Boris Tsirelson (talk) 18:12, 2 May 2016 (UTC)
On a side note: Gieres, F. (2000). "Mathematical surprises and Dirac's formalism in quantum mechanics". Rep. Prog. Phys. 63: 1893–1931. arXiv:quant-ph/9907069.  YohanN7 (talk) 16:54, 2 May 2016 (UTC)
Woooooow! Boris Tsirelson (talk) 18:12, 2 May 2016 (UTC)

Rearrangement of sections[edit]

On one hand, it is nice to pin down all mathematical and physical properties/requirements first thing (after the history).

On the other hand, it would be easier for typical readers to just see what the wave function is with examples, and the mathematical details later. Also, since the probability interpretation is what most sources present that section could be moved further up. The Hydrogen atom content in the function spaces section has been moved to the section of that example.

I tried to rearrange to see how it looks, and will not make further edits. Anyone is free to revert if they disagree. MŜc2ħεИτlk 06:50, 3 May 2016 (UTC)

Well, this happened. But anyone can revert to this version. MŜc2ħεИτlk 12:37, 3 May 2016 (UTC)

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