Talk:Mathematical formulation of quantum mechanics

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Summary table

what do people think of adding this summary table? someone wrote it for the List of elementary physics formulae article. I didn't wan't to completley delete it as its someone else's work and could have a place in the right article.

Postulate 1: State of a system	A system is completely specified at any one time by a Hilbert space vector.
Postulate 2: Observables of a system	A measurable quantity corresponds to an operator with eigenvectors spanning the space.
Postulate 3: Observation of a system	Measuring a system applies the observable's operator to the system and the system collapses into the observed eigenvector.
Postulate 4: Probabilistic result of measurement	The probability of observing an eigenvector is derived from the square of its wavefunction.
Postulate 5: Time evolution of a system	The way the wavefunction evolves over time is determined by Schrödinger's equation.

I really don't mind what the answer is by the way - its not my table:

$|\mathrm {answer} \rangle =y|\mathrm {yes} \rangle +n|\mathrm {no} \rangle ,\,\!$

just thought I would make the proposal.

F=q(E+v^B) (talk) 21:38, 24 November 2011 (UTC) — Preceding unsigned comment added by F=q(E+v^B) (talk • contribs) [reply]

Observations

I just wanted to point out a couple difficulties I am having with this article:

It's not clear to me what the scope of this article is with respect to quantum mechanics versus quantum field theory. Is the article trying to capture the formalisms for both? Could there be a separate article for the formalisms of QFT? They seem to run together in the article, and IMO, it makes the article less succinct than it could be.
In a similar way, the article seems to be conflicted about whether it should describe interpretations of quantum mechanics. My feeling is that this article is about the formalisms, so interpretations are out of scope, except in passing. I believe there are already articles about interpretations, so why not shift the interpretational concerns to those articles?

Postulates cleanup

Many thanks to User:GravitonsAndGraviolis for cleaning up the postulates. It was a mess of postulates, theorems, definitions, and interpretations, and now it its actually a list of the postulates used in the traditional axiomatization. Tercer (talk) 09:32, 14 March 2021 (UTC)[reply]

I don't think the postulates are adequately cited. For the whole collection, there is the statement: "The following summary of the mathematical framework of quantum mechanics can be partly traced back to the Dirac–von Neumann axioms." (citing Cohen-Tannoudji, Claude (2019)) and for the composite system postulate, there is a reference to Jauch, J. M.; Wigner, E. P.; Yanase, M. M. (1997). Apart perhaps from the composite system postulate, the postulates seem to have been formulated by wikipedians, rather than cited by wikipedians from primary or secondary sources. This strikes me as original research WP:NOR. 86.159.18.215 (talk) 11:50, 21 September 2022 (UTC)[reply]

Profoundly confusing

One passage reads as follows:

"Quantum states can be identified with equivalence classes in H, where two vectors (of length 1) represent the same state if they differ only by a phase factor. As such, quantum states form a ray in projective Hilbert space, not a vector."

This is profoundly confusing, because there is no such thing as a "ray" in a projective space.

Projective space is the result of identifying each linear subspace of some vector space, minus its zero element, to a single point. So it has no rays.

And, this directly contradicts the first quoted sentence above, because that states that two states are equivalent when they differ by a phase factor, i.e., scalar multiplication by a complex number of the form e^i𝜃 for some angle 𝜃 ∈ [0, 2π).

A ray is an equivalence class whose members differ by scalar multiplication by a nonnegative real number.

So multiplication by any complex number of norm 1 does not result in a "ray" in the mathematical sense.

I hope someone knowledgeable about this subject can fix this. — Preceding unsigned comment added by 2601:204:f181:9410:3d0c:fade:cf7f:7611 (talk) 15:50, 24 February 2025 (UTC)[reply]

The content has sources, your post does not. Johnjbarton (talk) 15:52, 24 February 2025 (UTC)[reply]