Expectation Values $<r^p>$ for Harmonic Oscillator in $R^n$

Ricardo Cordero-Soto, Sergei K. Suslov

Published 2009-08-01, updated 2009-08-06Version 3

We evaluate the matrix elements $<r^{p}>$ for the $n$ -dimensional harmonic oscillator in terms of the dual Hahn polynomials and derive a corresponding three-term recurrence relation and a Pasternack-type reflection relation. A short review of similar results for nonrelativistic hydrogen atom is also given.