Green's Function for the Quartic Oscillator

Robert L. Anderson
2016 Applied Mathematics  
In this paper, a quantum mechanical Green's function ( ) qo b b a a G y t y t , ; , 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 ( ) qo b b a a S y t y t , ; , in terms of harmonic oscillator
more » ... ic oscillator variables is derived in order to facilitate the derivation of the quartic oscillator Green's Function, namely in fixing its amplitude.
doi:10.4236/am.2016.714135 fatcat:r2ywvx427rbs5mq6fnfgfbemj4