Perturbation theory with canonical transformations

1 February 1992

journal article
research article
Published by American Physical Society (APS) in Physical Review A

Vol. 45 (3) , 1333-1338
https://doi.org/10.1103/physreva.45.1333

Abstract

I develop an alternative approach to the Rayleigh-Schrödinger perturbation theory that is based on a canonical transformation of the unperturbed operator into a first-order differential operator. As a result the perturbation formulas reduce to a hierarchy of first-order inhomogeneous differential equations that one can easily solve by quadratures for all the states simultaneously. I apply the method to the anharmonic oscillator, a perturbed Kratzer potential, and the LoSurdo-Stark effect in a two-dimensional hydrogen atom.

Keywords

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