Articulo
Small-energy series for one-dimensional quantum-mechanical models with non-symmetric potentials
Autor
Amore, Paolo
Fernández, Francisco Marcelo
Institución
Resumen
We generalize a small-energy expansion for one-dimensional quantum-mechanical models proposed recently by other authors. The original approach was devised to treat symmetric potentials and here we show how to extend it to non-symmetric ones. Present approach is based on matching the logarithmic derivatives for the left and right solutions to the Schrödinger equation at the origin (or any other point chosen conveniently). As in the original method, each logarithmic derivative can be expanded in a small-energy series by straightforward perturbation theory. We test the new approach on four simple models, one of which is not exactly solvable. The perturbation expansion converges in all the illustrative examples so that one obtains the ground-state energy with an accuracy determined by the number of available perturbation corrections. Instituto de Investigaciones Fisicoquímicas Teóricas y Aplicadas