A NOTE ON THE SCHRODINGER-EQUATION FOR THE X2 + LAMBDA-X2/(1 + GX2) POTENTIAL

The energy levels and wave functions of the Schrödinger equation involving the potential x2 + λx2/(1 + gx 2) are calculated by the variational method, for any range of λ and g, without having to resort to numerical quadrature. Using properly scaled (in λ and g) harmonic oscillator functions as a basis set, an easy to compute analytical expression of the current Hamiltonian matrix element is derived. Perturbative results are also given. © 1980 American Institute of Physics.