A new approach to the logarithmic perturbation theory for the spherical anharmonic oscillator

Details A new approach to the logarithmic perturbation theory for the spherical anharmonic oscillator A new approach to the logarithmic perturbation theory for the spherical anharmonic oscillator

2004-07-22

arxiv.org/abs/quant-ph/0407182v1

Physics

Quantum Physics

Submitted to Journal of Physics A: Math. and Gen

Scientific paper

The explicit semiclassical treatment of the logarithmic perturbation theory for the bound-state problem for the spherical anharmonic oscillator is developed. Based upon the $\hbar$-expansions and suitable quantization conditions a new procedure for deriving perturbation expansions is offered. Avoiding disadvantages of the standard approach, new handy recursion formulae with the same simple form both for ground and excited states have been obtained. As an example, the perturbation expansions for the energy eigenvalues of the quartic anharmonic oscillator are considered.

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