Semiclassical inversion of a symmetric double well potential

Abstract

An RKR based inversion procedure for a symmetric double well potential is developed and tested for a model system giving rise to four doubled energy levels below the barrier maximum. Two phase integral functions are extracted from the eigenvalue spectrum, one of which depends on the potential well and the other on the potential barrier and these two functions are then subjected to conventional RKR manipulation. The model potential is reproduced within a few per cent over most of the energy range and the height of the barrier is determined within one per cent.