Let's consider eigenstates [tex] |nlm\rangle [/tex] of hamiltonian of hydrogen atom.(adsbygoogle = window.adsbygoogle || []).push({});

Can anyone prove that

[tex] \langle r \rangle = \langle nlm|r|nlm\rangle = \frac{a}{2}(3 n^2-l(l+1))[/tex].

Where a - bohr radious.

I've been trying to prove it using some property of Laguerre polynomials (which are

radial part of eigenstates) but I stucked in it.

I found this equation in "Princliples of QM" by Shankar

(unfortunately with neither proof nor hint).

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# Formula for expectation value of raidous in Hydrogen atom

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