2016/05/04 by Anderson, Robert L.
#FOS: Physical sciences #Mathematical Physics (math-ph)
paper · doi:10.48550/arxiv.1605.01419
In this paper, a quantum mechanical Green's function Gqo(yb,tb; ya,ta) 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 Sqo(yb,tb; ya,ta) in terms of harmonic oscillator variables is derived in order to facilitate the derivation of the quartic oscillator Green's Function amplitude. Thus, the papers [1] and [2] and this paper, taken together, result in the incorporation of the quartic oscillator into the non-relativistic quantum mechanical physics literature consisting of those single particle systems whose properties are described in terms of trig functions, their quadratures or both.