Padé approximants and perturbation theory for screened Coulomb potentials

1981 ◽  
Vol 23 (2) ◽  
pp. 455-460 ◽  
Author(s):  
C. S. Lai
Keyword(s):  
Perturbation Theory ◽  
Padé Approximants ◽  
Pade Approximants ◽  
Screened Coulomb Potentials ◽  
Coulomb Potentials

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.

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.

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