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′.

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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