WKB solutions of the Schrödinger equation with a quartic potential

Abstract

The Schrödinger equation with a quartic potential is a fundamental equation describing the physics of stimulated side scattering, but no exact, even approximate solution has been formulated yet. Here, the approximate solutions to such a Schrödinger equation are derived using the WKBJ method under different variables. The solutions are accurate enough in most cases. Eigenvalues and eigenfunctions, which are the most impressive properties of such equations, are also discussed.