Small g and large λ solution of the Schrodinger equation for the interaction λx²/(1+gx²)

Abstract

Using perturbation theory, asymptotic expansions are derived for the eigenenergies and eigenfunctions of the wave equation for the interaction lambda x2/(1+gx2) in the range of small values of g and large values of lambda . The first few energy eigenvalues are calculated and found to be comparable with the non-perturbative results obtained by Mitra (1978).