On the radius of convergence of Rayleigh-Schrodinger perturbative solutions for quantum oscillators in circular and spherical boxes
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1983-12-01
Autores
Aguilera-Navarro, V. C.
Gomes, J. F.
Zimerman, A. H.
Ley Koo, K.
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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.
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Journal of Physics A: Mathematical and General, v. 16, n. 13, p. 2943-2952, 1983.