Simple procedure to compute accurate energy levels of a double-well anharmonic oscillator

Abstract

Accurate eigenvalues of the double-well anharmonic oscillator ($H={p}^{2}\ensuremath{-}{Z}^{2}{x}^{2}+{x}^{4}$) are obtained in all regimes of the coupling constant ${Z}^{2}$. Tables of some eigenvalues up to ${Z}^{2}\ensuremath{\le}100$ are presented. The method is nonperturbative and involves the use of an appropriately scaled harmonic basis.