WKB Approach to Calculating the Lifetime of Quasistationary States

Abstract

A novel WKB approach to calculating the lifetime of quasistationary states in the potential wells of the form V(x)=P(x)-muQ(x), where P(x) is the radial part of the potential for the spherically symmetric harmonic oscillator or the hydrogen atom and Q(x) is a polynomial, is suggested. In this approach, the usual explicit procedure of the asymptotic matching of the perturbative and WKB wave functions is avoided and a simple formula for the imaginary part of the energy is found. The leading and the first correction terms for the imaginary part of the energy and the related lifetime are analytically calculated.