Introduction to Quantum Mechanics · Problem 4.17

Quantum Mechanics in Three Dimensions — David J. Griffiths

Physics — Quantum Mechanics · hydrogen_operator_expectation

Problem

Calculate ⟨zH^z⟩\langle z \hat{H} z \rangle, in the ground state of hydrogen. Hint: This takes two pages and six integrals, or four lines and no integrals, depending on how you set it up. To do it the quick way, start by noting that [z,[H,z]]=2zHz−Hz2−z2H[z,[H,z]] = 2zHz - Hz^2 - z^2H.

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