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

A simple approximate solution for the quantum-mechanical quartic oscillator V = m(2)x(2) vertical bar gx(4) in the double-well regime m(2) < 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 less than or similar to 10(-3).