A unified treatment of Schrodinger's equation for anharmonic and double well potentials

Abstract

The authors exploit some exact soluble model potentials VN( alpha , beta )=V(A,B)+ lambda x6 in order to extrapolate (as lambda to 0) reliable eigenvalues of the one-dimensional Schrodinger equations with either anharmonic or symmetric double well potentials of the form V(A,B)=1/2Ax2+Bx2 (B>0). Their procedure, which corresponds to low-order Rayleigh-Schrodinger perturbation theory, is found to be competitive with both high-order Pade summation of conventional RSPT and large-scale variational calculations using harmonic oscillators basis functions.