Potential merge with expected value

This concept seems not the least bit different from the one treated in expected value. Only the terminology and some of the notation are different, this one perhaps reflecting conventions prevailing among some physicists. Michael Hardy 23:23, 24 May 2007 (UTC)[reply]

I was the one who split it out from the main expected value section. This was for 2 reasons: firstly, where it was placed in that article originally was clearly not the right place for the content. If it were to be on that page, it should be much lower down. However, secondly, one needs to have quite a lot of physics background to understand the explanation in this section, as evidenced by the current need for a physics expert to verify the content. The expected value article, on the other hand is currently (and I believe, should be) an introduction to the basic concept and some of its properties. Now, from this article, it seems to me that the expectation value of an operator is the expected value of some random variable, but it is not clear to me what that variable is. Thus, I believe that either (a) the expectation value concept in quantum mechanics is a concept which is closely related to that of an expected value, in which case it deserves its own page, or (b) it is just an application of the expected value concept for a certain variable, in which case I would be happy for it to be added to the applications section (or an examples section) of expected value, with it clearly spelt out what r.v.'s expected value we are dealing with. --Steve Kroon 06:15, 25 May 2007 (UTC)[reply]

You are correct in that this is related to the mathmatical method of expected value but this is a ratere important subject in Q.M. and deserivers to have the page expanded into a fuller treatment of ther subject. I will attempt to do so somewhat soon but I think the best solution would be a link to the page on expected value. Blue loonie 07:24, 10 June 2007 (UTC)[reply]

Excellent. I agree with the statement from Blue loonie above, this is certainly an important subject in Quantum Mechanics. While it is somewhat related to the expected value in mathematics, it's implication is very different. I'll also attempt to help with updating this article but we'll see how much time I get to do this. If anyone is watching this and can give an outline of what improvements/details should be included, please list them here. --JT 01:37, 16 August 2007 (UTC)[reply]

Details

The article currently says this:

The expectation value,

\langle x\rangle \,

of an operator,

{\hat {X}}\,

, operating on a wavefunction

\psi

is given by

x={\frac {\int _{-\infty }^{\infty }~\psi ^{*}{\hat {X}}\psi ~dV}{\int _{-\infty }^{\infty }~\psi ^{*}\psi ~dV}}.

Shouldn't it say something like the following?

The expectation value,

x=\langle {\hat {X}}\rangle \,

of an operator,

{\hat {X}}\,

, operating on a wavefunction

\psi

is given by

x={\frac {\int _{-\infty }^{\infty }~\psi ^{*}{\hat {X}}\psi ~dV}{\int _{-\infty }^{\infty }~\psi ^{*}\psi ~dV}}.

As it is, it says the expectation value is called $\langle x\rangle \,$ , but the operator is not called $x\,$ , but rather is called ${\hat {X}}$ , and then the "displayed" identity does not say " $\langle x\rangle =\cdots \,$ ", but instead says " $x=\cdots \,$ . Michael Hardy 20:37, 25 May 2007 (UTC)[reply]