Logarithmic perturbation theory for radial Klein-Gordon equation with screened Coulomb potentials via $\hbar$ expansions

Details Logarithmic perturbation theory for radial Klein-Gordon equation with screened Coulomb potentials via $\hbar$ expansions Logarithmic perturbation theory for radial Klein-Gordon equation with screened Coulomb potentials via $\hbar$ expansions

2002-12-14

arxiv.org/abs/quant-ph/0212087v1

International Journal of Modern Physics A, Vol. 19, No. 22 (2004) 3669-3683

Physics

Quantum Physics

14 pages, to be submitted to Journal of Physics A

Scientific paper

10.1142/S0217751X0401955X

The explicit semiclassical treatment of logarithmic perturbation theory for the bound-state problem within the framework of the radial Klein-Gordon equation with attractive real-analytic screened Coulomb potentials, contained time-component of a Lorentz four-vector and a Lorentz-scalar term, is developed. Based upon $\hbar$-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 for the Hulth\'en potential containing the vector part as well as the scalar component are considered.

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