A general expression for matrix elements of reciprocal powers of the displacement coordinate q in the harmonic oscillator basis

摘要

A formula is derived that allows one to determine the matrix elements of an arbitrary integral reciprocal power of the dimensionless displacement coordinate q of the harmonic oscillator from those of q~(-1) in an exact manner. This relation is obtained from the use of the chain rule and irreducible tensors expressed in terms of the creation and annihilation operators of the harmonic oscillator.