On a Flexible Double Minimum Potential

Abstract

Abstract The Gauss-perturbed harmonic oscillator, a customary double minimum potential of molecular spectroscopy, is made more flexible by addition of a term α4 · exp(-γ4X4). The matrix elements of the additional term are calculated in the harmonic oscillator basis in terms of parabolic cylinder functions. A sum rule for matrix elements serves as an independent numerical control. The eigenvalues can be given by straightforward diagonalization of the Hamilton-matrix. In addition, upper and lower bounds are given for the partition function.