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Applies to questions of primarily educational value - not only questions that arise from actual homework assignments, but any question where it is preferable to guide the asker to the answer rather than giving it away outright. Please READ THE GUIDANCE IN META before asking homework-like questions.

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Expectation value of $p^2 (1/r) + (1/r) p^2$

I'm trying to derive $\langle kl | \lbrace 1/r , p^2 \rbrace | nl \rangle$, where the states satisfy the equation of motion (I omit factors of $1/2m$ etc.): $$(p^2 + V)| n,l \rangle = E_n | n,l \rang …