Talk:Wave function/Archive 8: Difference between revisions

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:::::::::::... the matter wave

:::::::::::::::<math>\psi (\boldmathbf r_2, \tau_2) = \int K (\boldmathbf r_2 - \boldmathbf r_1; t_2 - t_1) \psi (\boldmathbf r_1, t_1) \, \mathrm d \boldmathbf r_1\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, (1)</math>

:::::::::::where

:::::::::::::::<math>K(\boldmathbf r, \tau) \,\,\,= (2\pi \hbar)^{{-3}} \int \exp \left [\frac {\mathrm i}{\hbar}(\boldmathbf p \cdot \boldmathbf r - E \tau)\right] \mathrm d \boldmathbf p.</math><ref>[[Albert Messiah|Messiah, A.]] (1958/1961). ''Quantum Mechanics'', volume 1, translated by G.M. Temmer from the French ''Mécanique Quantique'', North-Holland, Amsterdam, p. 75.</ref>

::::::Messiah does not feel a need for the ordinary-language word 'explicit' here because the situation seems obvious to him from what he has written, and he is not using the Dirac notation at that point, so as to need a contrast. I think for clarity for our purpose here an ordinary language word is needed to distinguish the two forms of expression. I did not invent the more technical term 'symbolic'; that is Dirac's. A symbolic expression is, for example, in Dirac's notation, |{{math|''z''}}〉 = {{math|''ζ''₁}}|{{math|''z''₁}}〉 + {{math|''ζ''₂}}|{{math|''z''₂}}〉 .

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::::::Weinberg in his ''Lectures'', on page 34, explicitly expresses a wave function as a function thus:

::::::::::::::::<math>\psi (\boldmathbf x) \,\,\,\,\,= R(r)Y(\theta,\phi) ,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, (2.1.21)</math><ref>[[Steven Weinberg|Weinberg, S.]] (2013). ''Lectures on Quantum Mechanics'', Cambridge University Press, Cambridge UK, {{ISBN|978-1-107-02872-2}}, p. 34.</ref>

'''References'''

{{Reflist}}

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::::::The kinds of experiments we shall consider are limited in the following respects: they are repeatable; there is a clear distinction between the state preparation device and the detection and registration device; and - this the most important limitation - we assume that for a given state-preparation device, preparing the system to be measured in a definite initial state, the state can be resolved into ''channels'', each of which can be independently blocked, in such a way that when only one channel is open the outcome of the experiment is ''deterministic'' - in the sense that if there is any registered outcome at all (on repetition of the experiment) it is always the ''same'' outcome.<ref>[[Simon Saunders|Saunders, S.]] (2004). 'Derivation of the Born rule from

operational assumptions', ''Proc. Roy. Soc. A'', '''460''': 1-18.</ref>
{{Reflist}}

::[[User:Chjoaygame|Chjoaygame]] ([[User talk:Chjoaygame|talk]]) 10:49, 7 February 2016 (UTC)

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:Likely I am missing the main point here.

[[File:Quixo-panza.jpg|Don Quixote and Sancho Panza|right|thumb|250px|Don Quixote, his horse Rocinante and his squire Sancho Panza after an unsuccessful attack on a windmill. By [[Gustave Doré]].]]

:::::<small class="autosigned">—&nbsp;Preceding [[Wikipedia:Signatures|unsigned]] comment added by [[Special:Contributions/194.68.82.241|194.68.82.241]] ([[User talk:194.68.82.241|talk]]) 13:55, 10 February 2016 (UTC)</small><!-- Template:Unsigned IP --> <!--Autosigned by SineBot--> Re-posted by [[User:Chjoaygame|Chjoaygame]] ([[User talk:Chjoaygame|talk]]) 14:19, 10 February 2016 (UTC)

:But anyway, here's a start. "How do you characterize a "maximal commuting set of observables"?" I think this is standard phrasing, at least in some places. One starts with some choice of observable. Then one chooses another. If they commute, it stays; if they don't, it's out. Repeat until one can't find any more that commute. I suppose that seems rather rough and ready, and hardly convincing. I will forthwith have a look to check this. Or is this utterly missing the point?[[User:Chjoaygame|Chjoaygame]] ([[User talk:Chjoaygame|talk]]) 11:05, 10 February 2016 (UTC)

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:See [[Talk:Scalar projection#This article has gravely misled me, and helped to make me look foolish, because I thought that on such a simple matter, an article like this could be trusted.]][[User:Chjoaygame|Chjoaygame]] ([[User talk:Chjoaygame|talk]]) 12:59, 14 February 2016 (UTC)

:Also [[Talk:Basis (linear algebra)/Archive 1#customary terminology not clear in Wikipedia; local editors, heads up]].[[User:Chjoaygame|Chjoaygame]] ([[User talk:Chjoaygame|talk]]) 18:17, 14 February 2016 (UTC)

:Perhaps I went overboard with the ''mea culpa''. Looking a bit further, I get the impression that customs vary.[[User:Chjoaygame|Chjoaygame]] ([[User talk:Chjoaygame|talk]]) 19:26, 14 February 2016 (UTC)