Talk:Wave function/Archive 4

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Lead edits

It's just my opinion, although recent edits to the lead seem to have gone backwards in clarity.

1. Sbyrnes321 beat me to this at the end of this section. I don't know what a "quantum analyzer" is (a hypothetical or real particle detector?), and it was clearer to get the point across quickly and say "the wavefunction is a function of the all the position coords and time, or momenta and time" etc.
2. A previous concern by Quondum here was mathematical. Is the codomain of the wavefunction always the complex numbers? The statement "However, complex numbers are not necessarily used in all treatments" has been deleted.

It is tempting to revert back to this lead version, but others should input first. M∧Ŝc²ħεИ_τlk 17:57, 3 January 2015 (UTC)

Input. YohanN7 (talk) 18:49, 3 January 2015 (UTC)

To be a bit more precise. Chjoaygame, what is the point of rewriting the lead in an archaic style so that instead of the occasional lay-reader not understanding it, now nobody understands it? This is not the place to invent terminology. Even if Bohr and others might have used it, the language and tone of the early 1900's is inappropriate and not quite penetrable if you want to know what QM is about. It perhaps makes the thing easier to read, but it comes with the price of making it impossible to understand. If we have to compromise between readability and correctness, then correctness will always come out on top. An article about QM that makes you feel good because you understood every single word (in isolation) isn't necessarily good. YohanN7 (talk) 19:05, 3 January 2015 (UTC)

It seems, I know what is meant by "analyzers". Just observables. In the same spirit as I wrote in the previous section: 'it is hardly a good idea, to fix once and for all the "right" collection of "physically natural" observables'. Coordinates, yes; momenta, yes; but any other observable, still yes, provided that its spectrum is of multiplicity 1 (the squared momentum does not fit, for instance). Boris Tsirelson (talk) 19:28, 3 January 2015 (UTC)

Regardless, the whole lead is not better than it was before. "Quantum analyzer" is not a common term and isn't helpful when you can just say "observable", which is standard and useful terminology.

Just to add to my point 2 above: currently the lead now merely states:

"Other treatments of quantum physics have been proposed, for example by Louis de Broglie.[6]"

which is not helpful since yes there are other formulations of QM, but this is not the point. For this article it should state wavefunctions are not always complex-valued.

Also Chjoaygame, could we keep the discussion in this section from this point forward? Thanks, M∧Ŝc²ħεИ_τlk 19:40, 3 January 2015 (UTC)

"I don't know what a "quantum analyzer" is (a hypothetical or real particle detector?)" It's the device that splits the beam into eigenstates that are sent to their respective detectors, as noted above.

I have undone my edit as suggested by Maschen.

I was driven to make the now undone edit because I think the lead should make the point that the wave function must be defined with respect to the possible measurements. For example London and Bauer (1939): "The wave function it uses to describe the object no longer depends solely on the object, as was the case in the classical representation, but, above all, states what the observer knows and what, in consequence, are his possibilities for predictions about the evolution of the object. For a given object, this function, consequently, is modified in accordance with the information possessed by the observer."<translation by Wheeler, Zurek et al., page 218 of Wheeler and Zurek 1983.> I read the latter as a paraphrase of Bohr's injunction. In mathematical terms that translates to a requirement for the mathematical existence of at least one basis that refers directly to physical existence. London and Bauer's "modification" of the wave function is not an adjustment of its values; it is a restructuring of its functional nature. Also I think that it should be made clear that QM "measurement" is not measurement in the ordinary language sense, as emphasized by Bohr.Chjoaygame (talk) 20:18, 3 January 2015 (UTC)Chjoaygame (talk) 20:47, 3 January 2015 (UTC)

For reference here is the reversion.

Thanks, we do appreciate the good faith efforts, but writing something along historical lines is not usually helpful, since interpretations, terminology etc. moves on. It's just that overall, the writing was not well-written, right at in beginning paragraph you wrote about "adventures" (...??).

About "quantum analyzers", I started this thread at 17:57, you posted in this section at 18:21, so I hadn't seen what you meant. M∧Ŝc²ħεИ_τlk 20:54, 3 January 2015 (UTC)

For the last point of Maschen, which is really an aside in this thread, there is no need at all to in the lead make the point that wave functions aren't necessarily complex valued under exceptional circumstances. The exceptions fall into two classes. The first class are exceptional circumstances where the imaginary part happens to vanish (Some 1-d problems, Majorana fermions in a certain basis). No mention needed. The second class is when a mathematical framework is used to transform the complex wave functions (and the machinery, including the Schrödinger/Dirac/Whatever equations) to a more complex domain, such as the domain of geometric algebra. (Ironically, this case is covered by complex valued wave functions.) Neither of these exceptions need to be mentioned in the lead. Why? Well, the reader might ask - if the wave function isn't a vector of complex numbers, then what the hell is it? This is not the place to elaborate on such questions. This is making something difficult more difficult. Connoisseurs of geometric algebra might object, but introducing GA in the lead here is overdoing it. The wave function is always an array of complex-valued functions. The fact that you can turn it to something else in a one-one fashion is immaterial. If that wasn't the case, most every lead needs to be rewritten. YohanN7 (talk) 20:35, 3 January 2015 (UTC)

Agreed.Chjoaygame (talk) 20:41, 3 January 2015 (UTC)

I was trying to not exclude other formulations of QM or mathematical machinery. If people want to cut that part out entirely that's fine, up to them, just write it clear so that no-one will ask the question again in future. M∧Ŝc²ħεИ_τlk 20:54, 3 January 2015 (UTC)

I know of the previous discussion, and I thought myself the wording was an okay compromise back then. I have cut it out because I no longer think it is okay (too demanding for the reader). The place to reintroduce it is in a new subsection of one of the mathematical sections as just one more formalism. YohanN7 (talk) 21:09, 3 January 2015 (UTC)

I also removed the de Broglie-Bohm theory from the lead. It presence seemed to be motivated by that real numbers were used as opposed to complex numbers. (My taking is that de Broglie-Bohm theory is something over and above ordinary QM and has little to do with how it is represented in terms of numbers.) YohanN7 (talk) 21:20, 3 January 2015 (UTC)

Chjoaygame I think some of your edits have been good, just out of place. Some of it (the Stern-Gerlach thing) could, if edited, go elsewhere. But here is another point, "... the wave function must be defined with respect to the possible measurements...". No, this is not so. The interpretation of the wave function might have to be associated with something we can measure (or it wouldn't be accepted as an interpretation), but this is all POV. Granted, it is the POV of some great minds, but it isn't necessary to develop QM to involve measurements. YohanN7 (talk) 21:40, 3 January 2015 (UTC)
(Here's my POV: Nature couldn't care less whether we measure it or not. YohanN7 (talk) 21:42, 3 January 2015 (UTC))

And mine: Nature measures itself in some situations, and does not in others, and this makes the quantum/classical interface; we are just one form of decoherence makers. Boris Tsirelson (talk) 06:47, 4 January 2015 (UTC)

What you say here needs some replies, but not here and now. According to Feynman, nobody understands QM.Chjoaygame (talk) 00:06, 4 January 2015 (UTC)

And he was right. YohanN7 (talk) 01:39, 4 January 2015 (UTC)

I've not seen the history of edits, and the controversial assertion that measurement is intrinsic to the definition of a wave function clearly cannot be made. To make this assertion would be to imply that the concept would not apply at all in the many-worlds interpretation. This is enough reason to exclude it. —Quondum 16:56, 4 January 2015 (UTC)

Archiving

I might have screwed up when putting a MiszaBot template here. It did archive, but the gods themselves only know to where. YohanN7 (talk) 00:50, 12 January 2015 (UTC)

It filled up an old archive, Archive 2, then created Archive 3. Stuff still here. YohanN7 (talk) 11:02, 12 January 2015 (UTC)

Phase space

From article:

In the common formulations of quantum mechanics, the wave function is never a function of both the position and momentum of a particle at any instant, because of the Heisenberg uncertainty principle; if the position of the particle is known exactly, the momentum is not known at all, and vice versa. For a particle in 1d, we can never write a wave function as Ψ(x, p, t). Taken together, x and p are called phase space variables. However, it is possible to construct a phase space formulation of quantum mechanics, using different mathematics and physical interpretations, in a way that does not violate the uncertainty principle.

I think this may be misleading to some degree. See Quantum harmonic oscillator#Ladder operator method. YohanN7 (talk) 12:45, 14 January 2015 (UTC)

And in that example link where is the wavefunction a function of position and momentum? M∧Ŝc²ħεИ_τlk 13:42, 14 January 2015 (UTC)

Did you truly expect to find any? I wouldn't have put it as mildly as I did if there were any. YohanN7 (talk) 13:45, 15 January 2015 (UTC)

Then what is misleading? Yes, you can use both the position and momentum operators together to solve ladder-like problems like the quantum SHO (an incredibly boring system but nevertheless important and useful), but this has nothing to do with writing a wave function as a function of both position and momentum. M∧Ŝc²ħεИ_τlk 14:16, 15 January 2015 (UTC)

I think it actually does have something to do with it. It is an example of a canonical transformation. But this is of minor importance, I just thought the formulation was a bit to strong on the emphasis of never mixing x and p. The new rule should be to not mix (the classical quantities) a and a*. At least I think so, I haven't done the problem in years. The operators â and â^† certainly each commute with themselves. Then again, the virtue of Dirac's method is that the Schrödinger equation (corresponding to the a or a*, there should be one since there is one for both x and p) doesn't have to be solved. I am admittedly uncertain here, it was a long time ago I looked into this. YohanN7 (talk) 16:25, 15 January 2015 (UTC)

"Mixing" x and p is allowed for the operators (obviously e.g. commutation relations, orbital angular momentum). The wave function as a function of both position and momentum is a separate thing. What I mean is the wave function is not a function of the full phase space, but just position (and time, spin etc.) or momentum (and time, spin etc.). M∧Ŝc²ħεИ_τlk 18:08, 15 January 2015 (UTC)

I know what you mean. The article might put it too strongly. I believe there is a wave function depending on either a or a*, for a = cx + ikp (where c and k are constants) describing the dynamics equally well. Do you say this is wrong? YohanN7 (talk) 18:27, 15 January 2015 (UTC)

I don't know. Maybe it is possible somehow using canonical transformations? I have done them in the Hamiltonian formulation of classical mechanics, but never in quantum mechanics. It just doesn't make sense for the wave function to depend on x and p because of the uncertainty principle, and what becomes of the relation between position and momentum space wavefunctions (Fourier transform)? M∧Ŝc²ħεИ_τlk 18:51, 15 January 2015 (UTC)

Yes, canonical transformations is what I'm talking about, see post four levels up. It is a wave function of x and p in a sense. It is a wave function of the single variable cx + ikp, much like an analytical function is a function of x and y, constrained to z = x + iy, not a function of x and y varying independently, but still a function of x and y. Again, I don't say the formulation in the article is wrong, it just might be misleading, ruling out what we are discussing here. I have also not seen the motivation (in the article) that it is the HUP that would rule out Ψ(x, p, t). If I'm right here, you can have Ψ(x, p, t), it must just be constrained to be of the form Ψ(cx + ikp) which does depend on x and p. YohanN7 (talk) 19:21, 15 January 2015 (UTC)

For now, best to delete the phase space section. It can be re-introduced later. There is no motivation for the exclusion in this article since the section is just a short digression, but how could you have a function of two observables which do not commute (in this case x and p)? If you know all the position coordinates how do you know the momenta? What meaning does Ψ(cx + ikp) have then? I don't know. If you have a source it may be interesting to add this to the article. M∧Ŝc²ħεИ_τlk 19:39, 15 January 2015 (UTC)

The supposed wave function is not a function of variables whose canonically associated operators do not commute. From above, the operators â and â^† certainly each commute with themselves (because every operator commutes with itself). No wave function Ψ(a, a*) exists (probably because â and â^† do not commute). Few things in QM have a sensible interpretation, this is quite general.

This is not intended for the article. Do you see now why the section of (the previous version of) the article could be misunderstood, provided I am right? YohanN7 (talk) 20:37, 15 January 2015 (UTC)

Maybe it is misleading, but I can't see the point in debating this further. M∧Ŝc²ħεИ_τlk 21:16, 15 January 2015 (UTC)

Then don't reply is a manner sneezing me off as your final comment. YohanN7 (talk) 21:48, 15 January 2015 (UTC)

tensor product

I am puzzled by the deletion of the definition of tensor product. It seems to me that the tensor product is of deep conceptual importance for quantum mechanics. For example, I think Elliot Leader's above-quoted statement, using the tensor product, is helpful in clarifying what you have been discussing about how to represent spin states. I accept that in a sense he is there not using it to combine states of distinct systems. I think it has also far wider use.Chjoaygame (talk) 02:21, 16 January 2015 (UTC)

Originally I intended to take the reader up to speed with the operation in the context of this article, before it is used later for the many particle states and position-spin states afterwards, but in the end it looked just like the tensor product section in the bra-ket article.

But perhaps it can be rewritten better, so let's reinstate it. In case there is strong consensus to delete it can be deleted again. M∧Ŝc²ħεИ_τlk 10:56, 16 January 2015 (UTC)

The tensor product section should definitely precede the multi-particle sections, and possibly the spin section as well. YohanN7 (talk) 14:11, 16 January 2015 (UTC)