Double Well Potential: Perturbation Theory, Tunneling, WKB (beyond instantons)

Abstract

A simple approximate solution for the quantum-mechanical quartic oscillator $V=m^2{x}^2+g{x}^4$ in the double-well regime $m^2<0$ at arbitrary $g\ge 0$ 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 $\lesssim 10^{-3}$.

13 pages, invited talk at "Crossing the boundaries: Gauge dynamics at strong coupling (Shifmania)", Minneapolis, May 14-17, 2009

References in corpus (2)

• Multi-Instantons and Exact Results II: Specific Cases, Higher-Order Effects, and Numerical Calculations
• Anharmonic oscillator and double-well potential: approximating eigenfunctions

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