Titlebook: Large Order Perturbation Theory and Summation Methods in Quantum Mechanics; G. A. Arteca,F. M. Fernández,E. A. Castro Book 1990 Springer-V

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The Semiclassical Approximation and the JWKB Methodmethods to obtain eigenfunctions, eigenvalues and expectation values of observables. The semiclassical methods make up a very valuable tool to get such information and their origin can be traced back to the birth of Quantum Mechanics. A renew interest has arisen during the last 20 years and today they have a remarkable relevance and currentness.

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Geometrical Connection Between the VFM and the JWKB Methodcal relationships, and the Heisenberg inequalities or the de Broglie hypothesis. It has been shown that all these approximations lead to eigenvalues depending on quantum numbers and parameters contained within the Hamiltonian, similarly to those obtained via the JWKB method and the variational theorem /1–13/ (see Chapter VI).

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Rayleigh-Schrodinger Perturbation Theory (RSPT)We devote this Section to present RSPT in a way appropriate to our specific needs. There are several alternative manners to introduce this formalism which can be found in the standard literature /1–3/.

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Divergence of the Perturbation SeriesThe RSPT (Chapter III) allows one to get an approximation to the eigenvalues (E.) of a given Hamiltonian operator through a series in powers of a real parameter λ. However, the usefulness of the power series is conditioned by a fundamental question: its convergence.

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