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In the course of answering the OP's question, I came across the commutator

$$ \left[ p_k, \frac{x_k}{r} \right] $$

where ##r = (x_1 + x_2 + x_3)^{1/2}## and ##p_k## is the momentum operator conjugate to ##x_k##. It's easy to show that the commutator is

$$ -i \hbar \left( \frac{1}{r} - \frac{x_k^2}{r^3} \right) $$

by working in the position basis. My question is: Is there a more elegant way (i.e., independent of basis) of deriving this commutator?

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# I Commutator of p and x/r

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