V C Aguilera-Navarro et al 1983 J. Phys. A: Math. Gen. 16 2943 doi:10.1088/0305-4470/16/13/015
V C Aguilera-Navarro, J F Gomes, A H Zimerman and K Ley Koo
Show affiliationsThe 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.
03.65.Ge Solutions of wave equations: bound states
33C10 Bessel and Airy functions, cylinder functions, 0F1
81Qxx General mathematical topics and methods in quantum theory
Issue 13 (11 September 1983)
V C Aguilera-Navarro et al 1983 J. Phys. A: Math. Gen. 16 2943
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