Talk:Wave function/Archive 8: Difference between revisions

Revision as of 11:14, 9 March 2016

Revision as of 14:44, 22 July 2017

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

::::::::::::::::<math>\psi (\bold 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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:::::::German original (1932/1996), ''Mathematische Grundlagen der Quantenmechanik'', Springer, Berlin, ISBN-13: 978-3-642-64828-1, p. 79: "Einen Operator, der keine echten Fortsetzungen besitzt — der also an allen Stellen, wo er vernünftigerweise, d. h. ohne Durchbrechung des Hermiteschen Charakters, definiert werden könnte, auch schon definiert ist — nennen wir maximal. Wir haben also gesehen: nur zu maximalen Operatoren kann eine Zerlegung der Einheit gehören."[[User:Chjoaygame|Chjoaygame]] ([[User talk:Chjoaygame|talk]]) 04:41, 11 February 2016 (UTC)

:::::::Newton, R.G. (2002), in ''Quantum Physics: a Text for Graduate Students'', Springer, New York, {{ISBN |0-387-95473-2}}, writes on page 317: "Suppose that <math>\mathfrak V</math> is such that there is a maximal number of linearly independent vectors in it, i.e., given any set of non-zero vectors with more than <math>n</math> members, they must be linearly dependent. The number <math>n</math> is then called the dimension of <math>\mathfrak V</math>." He doesn't use it in that sense elsewhere in that book.[[User:Chjoaygame|Chjoaygame]] ([[User talk:Chjoaygame|talk]]) 16:31, 10 February 2016 (UTC)

:::::::Bransden, B.H., Joachain, C.J. (1989/2000), ''Quantum Mechanics'', second edition, Pearson–Prentice–Hall, Harlow UK, {{ISBN |978-0-582-35169-7}}, p. 641: "Until now we have considered quantum systems which can be described by a ''single'' wave function (state vector). Such systems are said to be in a ''pure state''. They are prepared in a specific way, their state vector being obtained by performing a ''maximal measurement'' in which all values of a complete set of commuting observables have been ascertained. In this chapter we shall study quantum systems such that the measurement made on them is not maximal. These systems, whose state is incompletely known, are said to be in ''mixed states''."[[User:Chjoaygame|Chjoaygame]] ([[User talk:Chjoaygame|talk]]) 20:32, 10 February 2016 (UTC)

:::::::[[Gennaro Auletta|Auletta, G.]], Fortunato, M., [[Giorgio Parisi|Parisi, G.]] (2009), ''Quantum Mechanics'', Cambridge University Press, Cambridge UK, {{ISBN |978-0-521-86963-8}}, p. 174: "From Sec. 1.3 and Subsec. 2.3.3 we know that the state vector |{{math|''ψ''}}〉 contains the maximal information about a quantum system."[[User:Chjoaygame|Chjoaygame]] ([[User talk:Chjoaygame|talk]]) 20:48, 10 February 2016 (UTC)

:::::::I Googled the phrase 'maximal set of commuting observables', and found [https://books.google.com.au/books?id=4ZwKCAAAQBAJ&pg=PA16&lpg=PA16&dq=maximal+set+of+commuting+observables+quantum+mechanics&source=bl&ots=ihL-ouMAoN&sig=iXg5Sm2CzApf0ZEKLZC0OsNO4Xk&hl=en&sa=X&ved=0ahUKEwiQg8GC6u7KAhVEkZQKHQ4qB_IQ6AEIMTAG#v=onepage&q=maximal%20set%20of%20commuting%20observables%20quantum%20mechanics&f=false this], and [https://books.google.com.au/books?id=lJaX2PsTxNoC&pg=PT94&lpg=PT94&dq=maximal+set+of+commuting+observables+quantum+mechanics&source=bl&ots=N7mHtcmXS9&sig=lIFMSkB-3JiMp3XG_yMjMaGqBAg&hl=en&sa=X&ved=0ahUKEwiQg8GC6u7KAhVEkZQKHQ4qB_IQ6AEILjAF#v=onepage&q=maximal%20set%20of%20commuting%20observables%20quantum%20mechanics&f=false also this], and [https://books.google.com.au/books?id=Xg2NZD73b4cC&pg=PA107&lpg=PA107&dq=maximal+set+of+commuting+observables+quantum+mechanics&source=bl&ots=XNpZbW3V-K&sig=hjtTtngz9OkXfbzrTtv2A4EeZA4&hl=en&sa=X&ved=0ahUKEwiQg8GC6u7KAhVEkZQKHQ4qB_IQ6AEIKjAE#v=onepage&q=maximal%20set%20of%20commuting%20observables%20quantum%20mechanics&f=false moreover this], and yet [https://books.google.com.au/books?id=eWdDAAAAQBAJ&pg=PA131&lpg=PA131&dq=maximal+set+of+commuting+observables+quantum+mechanics&source=bl&ots=5ICKajbc5X&sig=UHUeWc7xUNMAAFvJnAQlfR9MhMM&hl=en&sa=X&ved=0ahUKEwiQg8GC6u7KAhVEkZQKHQ4qB_IQ6AEIOTAI#v=onepage&q=maximal%20set%20of%20commuting%20observables%20quantum%20mechanics&f=false again this], and [https://books.google.com.au/books?id=v1owGsfiJcoC&pg=PA4&lpg=PA4&dq=maximal+set+of+commuting+observables+quantum+mechanics&source=bl&ots=k9hKAHG4-4&sig=wGW8ASjUSj6u_x9XrRjxzHZpvts&hl=en&sa=X&ved=0ahUKEwiQg8GC6u7KAhVEkZQKHQ4qB_IQ6AEIPDAJ#v=onepage&q=maximal%20set%20of%20commuting%20observables%20quantum%20mechanics&f=false now this].[[User:Chjoaygame|Chjoaygame]] ([[User talk:Chjoaygame|talk]]) 04:18, 11 February 2016 (UTC)

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:"And how is "a state vector is an [[equivalence class]] of wave functions"?" I would have thought that was a standard way of expressing the situation. I learnt it when I studied algebra. It seems to be assumed as common mathematical parlance by the writer of this sentence: "Assuming that the unchanging reading of an ideal thermometer is a valid "tagging" system for the equivalence classes of a set of equilibrated thermodynamic systems, then if a thermometer gives the same reading for two systems, those two systems are in thermal equilibrium, and if we thermally connect the two systems, there will be no subsequent change in the state of either one." The sentence was posted in [https://en.wikipedia.org/w/index.php?title=Zeroth_law_of_thermodynamics&diff=next&oldid=667219209 this] edit by respected Editor [[User:PAR|PAR]]. My usage intends that all the wave functions that belong to a particular state are interconvertible by a group of one-to-one mathematical transformations. That makes them members of an equivalence class. (The equivalence class has the structure of a Hilbert space, more or less.) I find this form of expression helpful to show the relation between wave functions and state vectors. It may or may not be so for others.[[User:Chjoaygame|Chjoaygame]] ([[User talk:Chjoaygame|talk]]) 09:39, 14 February 2016 (UTC)

:Well, it seems that I have led myself astray by looking in Wikipedia and Google. Looking at a textbook on my shelves that I forgot I had, I find that indeed, as you say, a component is there defined as a scalar. Bloom, D.M. (1979), ''Linear Algebra and Geometry'', Cambridge University Press, Cambridge UK, {{ISBN |0-521-21959-0}}, p. 98. I hardly need say this makes me look silly. I am sorry. I can only say I misled myself by looking in Wikipedia and Google. That's a lesson. Well, I can only say I am sorry. My only excuse can be that I wrote "I would suggest adjusting it slightly, to make it agree with Wikipedia definitions as follows: .... I am suggesting to use the term [[scalar projection]]." Evidently that was a mistake. Now checking more in Wikipedia, I find at [[Basis (linear algebra)]] that I did not look in right place in Wikipedia. Just for clarity here, I will repeat, I now agree that 'component' is suitable. I guess a link to [[Basis (linear algebra)]] might be a good idea.[[User:Chjoaygame|Chjoaygame]] ([[User talk:Chjoaygame|talk]]) 12:37, 14 February 2016 (UTC)

: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)