# Expectation value of the Hamiltonian [closed]

How to calculate expectation value of the Hamiltonian for hydrogen atom? $$\langle H \rangle_{\alpha l} \equiv \frac{\langle \psi_{\alpha l m}|H(r)| \psi_{\alpha l m}\rangle} {\langle \psi_{\alpha l m} |\psi_{\alpha l m}\rangle }$$ Where $$\psi_{\alpha l m}=r^le^{-\alpha r^2}Y^m_l(\theta,\phi)$$ and $$H(r)=-\frac{\hbar^2}{2m}\nabla^2-\frac{e^2}{r}$$

## closed as off-topic by garyp, Gert, Prahar, Kostya, Sebastian RieseJan 24 '16 at 0:19

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "Homework-like questions should ask about a specific physics concept and show some effort to work through the problem. We want our questions to be useful to the broader community, and to future users. See our meta site for more guidance on how to edit your question to make it better" – garyp, Gert, Prahar, Kostya, Sebastian Riese
If this question can be reworded to fit the rules in the help center, please edit the question.

• Do the math. I assume you know calculus or you wouldn't be considering this problem. – Lewis Miller Jan 23 '16 at 20:42
• Basically cross posted on mathematica.SE. – Simon Jan 24 '16 at 2:11