Anharmonic oscillator and double-well potential: approximating eigenfunctions

Abstract

A simple uniform approximation of the logarithmic derivative of the ground state eigenfunction for both the quantum-mechanical anharmonic oscillator and the double-well potential given by $V=m^2{x}^2+g{x}^4$ at arbitrary $g\ge 0$ for $m^2>0$ and $m^2<0$, respectively, is presented. It is shown that if this approximation is taken as unperturbed problem it leads to an extremely fast convergent perturbation theory.

14 pages, 3 figures, 2 tables

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