Rayleigh-Schrödinger perturbation theory at large order for radial Klein-Gordon equations

B. R. McQuarrie; E. R. Vrscay

doi:10.1103/PhysRevA.47.868

Rayleigh-Schrödinger perturbation theory at large order for radial Klein-Gordon equations

B. R. McQuarrie, E. R. Vrscay

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Abstract

The relativistic hypervirial and Hellmann-Feynman theorems for the Klein-Gordon (KG) equation are used to construct Rayleigh-Schrödinger (RS) perturbation expansions to arbitrary order. The method is applied to the KG equation for a particle in an attractive Coulomb-type vector potential with perturbing vector or scalar potentials of the form rk, k=1,2,.... In the scalar case, such potentials are confining and the RS expansions exhibit Stieltjes behavior for k1 and Padé summability for k=1,2.

Original language	English (US)
Pages (from-to)	868-875
Number of pages	8
Journal	Physical Review A
Volume	47
Issue number	2
DOIs	https://doi.org/10.1103/PhysRevA.47.868
State	Published - 1993
Externally published	Yes

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abstract = "The relativistic hypervirial and Hellmann-Feynman theorems for the Klein-Gordon (KG) equation are used to construct Rayleigh-Schr{\"o}dinger (RS) perturbation expansions to arbitrary order. The method is applied to the KG equation for a particle in an attractive Coulomb-type vector potential with perturbing vector or scalar potentials of the form rk, k=1,2,.... In the scalar case, such potentials are confining and the RS expansions exhibit Stieltjes behavior for k1 and Pad{\'e} summability for k=1,2.",

author = "McQuarrie, {B. R.} and Vrscay, {E. R.}",

year = "1993",

doi = "10.1103/PhysRevA.47.868",

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AB - The relativistic hypervirial and Hellmann-Feynman theorems for the Klein-Gordon (KG) equation are used to construct Rayleigh-Schrödinger (RS) perturbation expansions to arbitrary order. The method is applied to the KG equation for a particle in an attractive Coulomb-type vector potential with perturbing vector or scalar potentials of the form rk, k=1,2,.... In the scalar case, such potentials are confining and the RS expansions exhibit Stieltjes behavior for k1 and Padé summability for k=1,2.

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Rayleigh-Schrödinger perturbation theory at large order for radial Klein-Gordon equations

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