Quantum mechanical expectation value

[Master J]

I'm trying to calculate the expectation value of the momentum squared (p^2) of the harmonic oscillator ground state.

The integral involves the second derivative of a Gaussian (exponential of a negative squared term)

Then the integral involves, after working it out, an x^2 term times exp(-x^2).

I tried this by integrating by parts but it gets me no where. Am I missing something?

 

[Master J]

Wait, I solved it :p


If anyone is interestes, it's just the fact that the 2nd term is a derivative of a Gaussian!