# Expectation value question

Discussion in 'Physics' started by boks, Nov 16, 2008.

1. ### boks Thread Starter Active Member

Oct 10, 2008
218
0
If $\Psi (x,t) = \psi (x) g(t)$, should I then use $\Psi$ or $\psi$ when calculating $

$

and $

$

?

2. ### steveb Senior Member

Jul 3, 2008
2,432
469
mmm .... I'm not sure about this one. I can mention what I think, but take it with a grain of salt.

My guess is that you are expressing a time- and position-dependent wave function as a product of a position-dependent wave function and a time modifying function. I believe that QM just treats time as a parameter, so I think this is ok.

So, if you want to find the expected value of momentum (I'm assuming that $p$ stands for momentum) and evaluate the time dependence, then you should use the full function $\Psi (x,t)$.

One additional thought comes to mind. If you have a system where momentum is conserved, then it shouldn't matter which one you use.

Also, the function $g(t)$ would seem to be a special class of complex function that always has a magnitude of one. Otherwise, the wave function would not stay normalized. This fact may also have implications. For example, does this imply that momentum is conserved? I'm not sure. I can think of cases where this is true (for example a simple plane wave), and I can't think of a case where it isn't true, but that is not proof.

I guess I'm saying that it is safer to use the full function, but it may be unnecessary, and, if so, it would be simpler to use the spatial function only.

When you find out the answer for sure, will you tell me please? Thanks!

3. ### boks Thread Starter Active Member

Oct 10, 2008
218
0
It works with the spatial function.