On the radius of convergence of Rayleigh-Schrodinger perturbative solutions for quantum oscillators in circular and spherical boxes

• Autor(a) principal: Aguilera-Navarro, V. C.
• Data de Publicação: 1983
• Outros Autores: Gomes, J. F., Zimerman, A. H., Ley Koo, K.
• Tipo de documento: Artigo
• Idioma: eng
• Título da fonte: Repositório Institucional da UNESP
• Texto Completo: http://dx.doi.org/10.1088/0305-4470/16/13/015; http://hdl.handle.net/11449/230934

The energy eigenvalues of harmonic oscillators in circular and spherical boxes are obtained through the Rayleigh-Schrodinger perturbative expansion, taking the free particle in a box as the non-perturbed system. The perturbative series is shown to be convergent for small boxes, and an upper bound for the radius of convergence is established. Pade-approximant solutions are also constructed for boxes of any size. Numerical comparison with the exact eigenvalues-which are obtained by constructing and diagonalising the Hamiltonian in the basis of the eigenfunctions of the free particle in a box-corroborates the accuracy and range of validity of the approximate solutions, particularly the convergence and the radius of convergence of the perturbative series.