# Square of Laplace–Runge–Lenz vector in Hydrogen atom [closed]

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: $$\mathbf M^2 = (2H/\mu)(\mathbf L^2+ \hbar^2) + e^4$$

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## closed as too localized by David Z♦Feb 27 '12 at 1:45

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Welcome to Physics! This is a site for conceptual questions about physics, not general homework help. If you can edit your question to ask about the specific physics concept that is giving you trouble, I'll be happy to reopen it. See our FAQ and homework policy for more information. –  David Z Feb 27 '12 at 1:46
sorry about that. I'm new to this forum. I will do that the next time. –  Pishi Feb 27 '12 at 1:52
This is the quantum analog of the Lens-Thirring vector, and you should check the classical identity first. –  Ron Maimon Feb 27 '12 at 4:11
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