TITLE:
Green’s Function for the Quartic Oscillator
AUTHORS:
Robert L. Anderson
KEYWORDS:
Nonrelativistic, Quartic, Quantum, Mechanics, Green’s, Oscillator
JOURNAL NAME:
Applied Mathematics,
Vol.7 No.14,
August
25,
2016
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.