Semiclassical treatment of logarithmic perturbation theory

Details Semiclassical treatment of logarithmic perturbation theory Semiclassical treatment of logarithmic perturbation theory

1999-02-26

arxiv.org/abs/quant-ph/9902086v1

J.Phys.A32:563-568,1999

Physics

Quantum Physics

6 pages, LATEX 2.09 using IOP styles

Scientific paper

10.1088/0305-4470/32/3/011

The explicit semiclassical treatment of logarithmic perturbation theory for the nonrelativistic bound states problem is developed. Based upon $\hbar$-expansions and suitable quantization conditions a new procedure for deriving perturbation expansions for the one-dimensional anharmonic oscillator is offered. Avoiding disadvantages of the standard approach, new handy recursion formulae with the same simple form both for ground and exited states have been obtained. As an example, the perturbation expansions for the energy eigenvalues of the harmonic oscillator perturbed by $\lambda x^{6}$ are considered.

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