Gaussian wavefunction; expectation energy

[novop]

Homework Statement

Homework Equations

The Attempt at a Solution

The issue I'm having here is that the problem should be able to be done rather quickly. I can see how to solve for <H> using the operator, but there's a quick way that I'm not picking up on.

I thought about solving <H> = <p^2> / 2m, but getting <p^2> is just as much of a pain.

Any help ?

 

[CompuChip]

By definition,

$$\langle H \rangle = \int \psi^* \hat H \psi \, dx$$
where, as you said
$$\hat H = \frac{p^2}{2m}$$

and you should be able to do that using the second hint (remember that $p \propto \partial/\partial x$ in the position representation).