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Accurate summation of the perturbation series for periodic eigenvalue problems |
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| Authors: | FM Fernández CG Diaz |
| Institution: | (1) CEQUINOR (Conicet), Facultad de Ciencias Exactas, Universidad Nacional de La Plata, Calle 47 y 115, Casilla de Correo 962, 1900 La Plata, Argentina, AR;(2) Departamento de Quımica, Facultad de Ciencias Exactas y Naturales, Universidad Nacional de Mar del Plata, Funes 3350, 7600 Mar del Plata, Argentina, AR |
| Abstract: | We show that algebraic approximants prove suitable for the summation of the perturbation series for the eigenvalues of periodic problems. Appropriate algebraic approximants constructed from the perturbation series for a given eigenvalue provide information about other eigenvalues connected with the chosen one by branch points in the complex plane. Such approximants also give those branch points with remarkable accuracy. We choose Mathieu's equation as illustrative example. Received 6 December 2000 |
| Keywords: | PACS 03 65 Ge Solutions of wave equations: bound states – 32 60 +i Zeeman and Stark effects |
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