In this paper, a quantum mechanical Green's function $G_{qo}(y_b,t_b;$ $y_a,t_a)$ 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 $S_{qo}(y_b,t_b;$ $y_a,t_a)$ 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.

This paper has been withdrawn by the author due to many errors that need work