DOUBLE WELL POTENTIAL: PERTURBATION THEORY, TUNNELING, WKB (BEYOND INSTANTONS)

Abstract

A simple approximate solution for the quantum-mechanical quartic oscillator V = m2x2 + gx4 in the double-well regime m2 < 0 at arbitrary g ≥ 0 is presented. It is based on a combining of perturbation theory near true minima of the potential, semi-classical approximation at large distances and a description of tunneling under the barrier. It provides 9-10 significant digits in energies and gives for wavefunctions the relative deviation in real x-space less than ≲ 10-3.