Quasi-Harmonic Approximation in the Case of Potential Wells of Finite Depth

Abstract

The recently proposed quasi-harmonic approximation to wave functions of bound states is generalized and applied to the potential wells of a finite depth with two inflection points. The approximate eigenfunctions are expressed via parabolic cylinder functions. The realized verification in the case of the modified P¨oschl-Teller potential shows fairly high accuracy of the proposed approximation.