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?

Thanks in advance,
Vivek.

 

[malawi_glenn]

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 :-|