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 Riese Jan 24 '16 at 0:19

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