Energy approximants and perturbation theory for screened Coulomb potentials

1980 ◽  
Vol 58 (8) ◽  
pp. 1212-1215 ◽  
Author(s):  
C. S. Lai ◽  
D. Kiang
Keyword(s):  
Perturbation Theory ◽  
Numerical Integration ◽  
Virial Theorem ◽  
Yukawa Potential ◽  
Perturbation Series ◽  
Screened Coulomb Potentials ◽  
Energy Perturbation ◽  
Feynman Theorem ◽  
Coulomb Potentials ◽  
Good Agreement

By applying the Hellmann–Feynman theorem and the virial theorem to screened Coulomb potentials, the energy is shown to be expressible in terms of an integral. Making use of the Padé approximant for the integrand, the modified [3,4] energy approximant obtained speeds up to the convergence of the energy perturbation series. The prediction of the modified [3,4] energy approximant for an electron in the Yukawa potential is in good agreement with that of numerical integration.

On the logarithmic perturbation theory for screened Coulomb potentials

1982 ◽  
Vol 60 (3) ◽  
pp. 365-367
Author(s):  
C. S. Lai
Keyword(s):  
Perturbation Theory ◽  
Excited States ◽  
Ground State ◽  
Recurrence Relations ◽  
Screened Coulomb Potentials ◽  
Coulomb Potentials

The ground-state logarithmic perturbation theory for screened Coulomb potentials is extended to the case of excited states. For states with I = n – 1, the recurrence relations obtained provide a convenient scheme for calculating the energy coefficients E(k). This logarithmic scheme is compared with an exponential scheme developed earlier.

scholarly journals LOGARITHMIC PERTURBATION THEORY FOR RADIAL KLEIN–GORDON EQUATION WITH SCREENED COULOMB POTENTIALS VIA ℏ-EXPANSIONS

2004 ◽  
Vol 19 (22) ◽  
pp. 3669-3683
Author(s):  
I. V. DOBROVOLSKA ◽  
R. S. TUTIK
Keyword(s):  
Perturbation Theory ◽  
Gordon Equation ◽  
Bound State ◽  
Perturbation Expansions ◽  
Screened Coulomb Potentials ◽  
Lorentz Scalar ◽  
Klein Gordon ◽  
Bound State Problem ◽  
Klein Gordon Equation ◽  
Coulomb Potentials

The explicit semiclassical treatment of logarithmic perturbation theory for the bound-state problem within the framework of the radial Klein–Gordon equation with attractive screened Coulomb potentials, contained time-component of a Lorentz four-vector and a Lorentz-scalar term, is developed. Based upon ℏ-expansions and new quantization conditions a novel 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 Hulthén potential containing the vector part as well as the scalar component are considered.

Padé approximants applied to perturbation theory for the linear confining potential

1981 ◽  
Vol 59 (6) ◽  
pp. 733-736 ◽  
Author(s):  
C. S. Lai ◽  
W. C. Lin
Keyword(s):  
Perturbation Theory ◽  
Bound State ◽  
Padé Approximants ◽  
Perturbation Series ◽  
Energy Eigenvalues ◽  
Pade Approximants ◽  
Confining Potential ◽  
Energy Perturbation

By forming the [6,6] and [6,7] Padé approximants to the energy perturbation series for the linear confining potential, we calculate energy eigenvalues of the 1s, 2s–2p, 3s–3d, and 4s–4f states. The bound-state energies calculated are found to follow the order of levels: Enl < Enl′ for l > l′.

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