# Exceptation of energy by Hamiltonian

1. Jun 30, 2014

### axcelenator

Hello,

The question says that we can write the Hamiltonian of the harmonic oscilator like this:
H=0.5*[P^2/m + (4*h^2*x^2)/(m*σ^4)] where h is h-bar

I need to calculate the expectation value of energy of the oscilator with the next function: ψ(x)=A*exp{-[(x-bi)^2]/σ^2}.

I tried to the the integral: ∫ψ*Hψdx where H is the operator of p and x but I got a big integral and I dont think its the write way because the finite answer is pretty simple:
Answer: (h^2/m)*(1/σ^2 + (2*b^2)/σ^4) where h is h-bar

How can I solve it?
Thanks

Last edited: Jun 30, 2014
2. Jul 1, 2014

### king vitamin

I'm not sure there is a simpler way. Could you show us some of your work?

Also, you could consider a clever change of variables in the integrals (recall that you need to determine the constant A as well).