I have a problem. I've tried this question, but I don't get the correct expression. Can someone give me some ideas? Thanks!
Consider the Hydrogen Atom Hamiltonian:
$$ H = (\mathbf p^2/2 \mu)-(e^2/r) $$ Define a vector operator: $$ \mathbf M = (1/2 \mu)(\mathbf p\times\mathbf L - \mathbf L\times\mathbf p)-(e^2/r)\mathbf r $$
Show that: $$ \mathbf M^2 = (2H/\mu)(\mathbf L^2+ \hbar^2) + e^4 $$