# How to compute Hydrogen Inner Products <n,l+1,m+1|n,l-1,m+1>?

#### maverick280857

Hi,

I want to compute inner products of the form

$$\langle n,l+1,m+1|n,l-1|m+1\rangle$$

where $|n,l,m\rangle$ are hydrogen atom eigenfunctions.

Whats the best way to do this, without writing them in the position space representation (i.e. evaluating volume integrals)? Are there any known identities to do this calculation?

Vivek.

Last edited:
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#### malawi_glenn

Homework Helper
check that inner product once more, there is a misprint.

<n,L1,m1|n,L2,m2> = 0.

Distinct eigenfunctions are always orthogonal.

#### maverick280857

Yeah, I forget where . I had to determine coefficients of a linear combination containing these two kets. And to find them, I started taking inner products. Maybe I made some mistake.

Thanks for your reply, malawi_glenn. I'll post back with the right terms...I think I should sleep more :-|

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