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 qu asistationary states in spherically symmetric potential wells is suggested. Using this approach, a general formula for the imaginary part of the energ y for potentials of the form V(x) = P(x) - muQ(x) - where P(x) is the radia l part of the potential for a spherically symmetric harmonic oscillator and Q(x) is an even polynomial-is derived. Using this formula, the usual tedio us procedure of the explicit asymptotic matching of the WKB and perturbativ e wave functions is avoided, and calculations are substantially simplified. The leading term and a few corrections of the series for the imaginary par t of the energy and the related lifetime are analytically calculated.