How to Find the Expectation Value of Momentum?

[mogsy182]

Homework Statement

find expectation value of the momentum fro

SI(x,t) = (1/aPI)^1/4 exp((-x^2)/2a)

Homework Equations

pSI(x,t) = -ih dsi/dx
<SI*[p]SI> = integral SI*pSI dx

The Attempt at a Solution

just need help with the integral

 

[ozymandias]

I'm having a bit of trouble following your notation, but I'm guessing you're trying to calculate:

$$<P> = \int_{-\infty}^\infty \psi(p) p \psi^*(p) dp$$

where:

$$\psi(p) = \int_{-\infty}^\infty \psi(x) e^{\frac{\imath p x}{\hbar}} dx$$

Which integral do you need help with?

--------
Assaf
http://www.physicallyincorrect.com/"

 

[mogsy182]

yes its the first integral
Im following a soloution to a similar question in my notes and it says something about odd/even function? thanks

 

[ozymandias]

Have you calculated $$\psi(p)$$ yet? If so, what was your result? If not, let's start with that.

 

[mogsy182]

hope you get the notation lol
hopefully this is right

SI(p) = ih(1/aPI)^1/4 ((x/a)exp ((-x^2)/2a)))


what do you use to get the notation on the forum?

 

[dwintz02]

When you use the operator p on Psi in the integral, a factor of x will pop out when you take the derivative of Psi. Then you'll have something like x times e^(-x^2) and then you should use the properties of even and odd functions to simplify the integral greatly.

Hope that helps