# Table of matrix elements of powers of r for radial functions in H atom

Im looking for some references here. I hope it is the right place to ask.

I need to find a table of (or a formula from which to extrapolate) the matrix elements of the radial functions of the hydrogen atom evaluated in powers of $r$ for both diagonal and off-diagonal elements. That is, I need this guys:

$<R_{nl}|r^k|R_{n'l'}>$

I found this article http://iopscience.iop.org/0953-4075/28/3/007 which is great, but Im looking for something more textbook-like, say suited for undergrad. I especially need positive powers until k=4.

Any help is very appreciated.

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I do not think such a table exists. You can probably just hack the integral into Mathematica and retrieve the results. – Neuneck May 14 '13 at 12:40
That's what im doing now, thanks – user24273 May 15 '13 at 14:22

## 2 Answers

1. Bockaste.K(1974), MEAN-VALUES OF POWERS OF RADIUS FOR HYDROGENIC ELECTRON ORBITS. Physical Review A. 9(3): p. 1087-1089, DOI: 10.1103/PhysRevA.9.1087. This is the standard ref and has a table.
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Hello Steve, and welcome to Physics.SE! It would be very helpful to everyone involved if you stated and/or explained the content of your source. – Dave Coffman Mar 27 '15 at 19:51

In the closed form solution the radial component is given by one of the Laguerre polynomials the coefficients and properties of which are tabulated in many places such as Abramowitz and Stegun.

From this you can compute the values you want easily.

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Yea i know, i was just looking for a table. Anyway, thanks for that. – user24273 May 15 '13 at 14:22