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Modified the claim that Ballentine presents arguments for the actual derivation of Schrödinger's equation. Ballentine references and reproduces other work that "derives" certain results that are usually derived from analysis of Quantum Mechanics. Symmetry arguments result in commutation relations such as [G, P]=ih (page 76). I see no argument presented in Ballentine for the actual derivation of the equation itself. It is simply postulated that a physical variable is represented by a Hermitian operator, a Hermitian operator necessarily satisfies A|psi>=a|psi>. It is simply postulated that the eigenvalues and vectors of the operator are the only possible physical values. It is simply postulated that |psi> gives the probability. Kevin Aylward 09:06, 5 September 2015 (UTC) — Preceding unsigned comment added by Kevin aylward (talk • contribs)
Thanks for clearing it up. It was most likely the misunderstanding of whoever added the claim. M∧Ŝc2ħεИτlk 11:38, 5 September 2015 (UTC)
There is a lot more worse wrong with the whole article. I had one attempt to remove "proves particles takes two paths an once" but this was reverted. I don't have a lot of time to never ending correct all the blatant misconceptions. I am not sure the best way to tackle this comic book view of QM. So few understand that QM is a mathematical structure that predicts probabilistic results, and 99.9% of practitioners don't care a toss about waffle interpretations. All the waffle is a direct result of not accepting that QM is a new axiom of physics. It simply can not be explained by discussing which way some hypothetical entity may or may not travel. Classical reasoning always gets you contradictions, hence is false. Luboš Motl gets this bit spot on. I have a short wordy description here http://www.kevinaylward.co.uk/qm/quantum_mechanics.html, and reference Motl's page with the relevant math, although he is discussing a different problem. Kevin Aylward 14:31, 5 September 2015 (UTC) — Preceding unsigned comment added by Kevin aylward (talk • contribs)
In fact, the standard way of "deriving" the Schrödinger equation is as follows. First, we put some constraints on the time-evolution operator. The fact that norms in the Hilbert space have to be conserved, and that time-evolution leads to a group structure, implies that the time evolution operator has to be unitary. The Hamiltonian is then simply the Hermitian operator that generates this unitary evolution. If we then demand that the dynamics of the system reduce, in the classical limit, to classical dynamics, then it is possible to argue that the quantum Hamiltonian coincides with the classical Hamiltonian up to operator ordering ambiguities, of course. The argument above is quite standard in a graduate treatment. For example, see Sakurai, Modern Quantum Mechanics, p. 71. I'm not sure why this is not present in the article. Is this because editors had some deep philosophical objection to terming this argument a "derivation". Or is it simply not there, because no one put it there. If its the latter, then I'll try and add it to the article later today. Jacob2718 (talk) 16:18, 3 December 2016 (UTC)
It is looking great. Please do not forget to cite your source(s). Nerd271 (talk) 20:34, 13 December 2016 (UTC)
Apart from inserting a derivation of the equation (see above), I have also removed the incorrect statement that Schrödinger's equation is inconsistent with quantum field theory. Perhaps the editors who inserted this meant that it is impossible to write down a Hamiltonian for a single particle consistent with special relativity. However, quantum field theory is still based on Schrödinger's equation, except that the wave-function must be defined on the Fock space. Alternately, one may consider wave-functions on field configurations. In fact, even in extensions of quantum field theory like string theory, Schrödinger's equation is not modified. Jacob2718 (talk) 09:07, 4 December 2016 (UTC)
As per this talk page, the article is written in American English, where "nonrelativistic" seems to be more common (the Merriam-Webster dictionary lists the word as "nonrelativistic"). I have thus edited the article accordingly.Penskins (talk) 16:06, 8 January 2017 (UTC)
Does anyone think enough/a sufficient amount of content has been added since the last assessment in February 2008 to warrant a re-nomination of this article for Good Article status? HapHaxion (talk) 04:20, 22 March 2017 (UTC)
New section "Formulation without complex numbers"