WKB approach to calculating the lifetime of quasistationary states:: Harmonic oscillator in a polynomial perturbation -: art. no. 022107

A simple and straightforward WKB approach to calculating the lifetime of quasistationary states in spherically symmetric potential wells is suggested. Using this approach, a general formula for the imaginary part of the energy for potentials of the form V(x) = P(x) - muQ(x) - where P(x) is the radial part of the potential for a spherically symmetric harmonic oscillator and Q(x) is an even polynomial-is derived. Using this formula, the usual tedious procedure of the explicit asymptotic matching of the WKB and perturbative wave functions is avoided, and calculations are substantially simplified. The leading term and a few corrections of the series for the imaginary part of the energy and the related lifetime are analytically calculated.