Green’s Function for the Quartic Oscillator

Abstract

In this paper, a quantum mechanical Green’s function for the quartic oscillator is presented. This result is built upon two previous papers: first [1], detailing the linearization of the quartic oscillator (qo) to the harmonic oscillator (ho); second [2], the integration of the classical action function for the quartic oscillator. Here an equivalent form for the quartic oscillator action function in terms of harmonic oscillator variables is derived in order to facilitate the derivation of the quartic oscillator Green’s Function, namely in fixing its amplitude.