Padé approximants and perturbation theory for screened Coulomb potentials

Lai, C. S.

doi:10.1103/physreva.23.455

Cited by 91 publications

(43 citation statements)

References 13 publications

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“…Table IV presents the calculated eigenvalues of some representative states with n ≤ 6 at selected values of the screening parameter (weak and strong screenings in the left and right respectively). Lower states have been examined by many methods; e.g., Rayleigh-Schrödinger perturbation expansion [21], variational methods [6,15,16], Padé approximations [20], shifted 1/N expansions [22,25], numerical calculations through direct integration of the SE [30] or by the Ritz method [31], etc. Other works include [12,33].…”

Section: Resultsmentioning

confidence: 99%

“…Many formally attractive and efficient formalisms have been proposed for accurate determination of the eigenvalues, eigenfunctions as well as for the values of the critical screening parameters differing in complexity, accuracy and efficiency. The most notable of these are the variational calculations employing a multitude of basis functions [14][15][16][17][18]12], combined Padé approximation and perturbation theory [19][20][21], shifted 1/N approximation along with many of its variants [22][23][24][25][26][27], dynamical-group approach [28], supersymmetric quantum mechanics [29], numerical calculations [30][31]18] and other works [32][33].…”

Section: Introductionmentioning

confidence: 99%

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The generalized pseudospectral approach to the bound states of the Hulthén and the Yukawa potentials

Roy

2005

Pramana - J Phys

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The generalized pseudospectral method is employed to calculate the bound states of Hulthén and Yukawa potentials in quantum mechanics, with special emphases on higher excited states and stronger couplings. Accurate energy eigenvalues, expectation values and radial probability densities are obtained through a nonuniform and optimal spatial discretization of the radial Schrödinger equation. Results accurate up to thirteen to fourteen significant figures are reported for all the 55 eigenstates of both these potentials with n ≤10 for arbitrary values of the screening parameters covering a wide range of interaction. Furthermore, excited states as high as up to n = 17 have been computed with good accuracy for both these potentials. Excellent agreement with the available literature data has been observed in all cases. The n > 6 states of Yukawa potential has been considerably improved over all other existing results currently available, while the same for Hulthén potential are reported here for the first time. Excepting the 1s and 2s states of Yukawa potential, the present method surpasses in accuracy all other existing results in the stronger coupling region for all other states of both these systems. This offers a simple and efficient scheme for the accurate calculation of these and other screened Coulomb potentials. * Electronic address: akroy@unb.ca

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Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

The generalized pseudospectral approach to the bound states of the Hulthén and the Yukawa potentials

Roy

2005

Pramana - J Phys

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“…Moreover, the Yukawa potential is used in several branches of physics such as solid-state, atomic, and plasma physics. The Yukawa potential has been analyzed using several methods [5][6][7]. For g = 1 case, Eq.…”

Section: V(r) = −mentioning

confidence: 99%

Application of the asymptotic iteration method to the exponential cosine screened Coulomb potential

Bayrak

Boztosun

2006

Int J of Quantum Chemistry

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ABSTRACT:We present the iterative solutions of the radial Schrödinger equation for the exponential cosine screened Coulomb (ECSC) potential for any n and l quantum states by applying the asymptotic iteration method (AIM). We show that it is possible to obtain the solution as accurate as the other methods without any perturbation. Furthermore, there are no tedious mathematical difficulties and restrictions on finding the energy eigenvalues for any n and l quantum numbers. Our results are in excellent agreement with the ones published in the literature.

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“…It has also been shown that the problem of screened Coulomb potentials can be solved to a very high accuracy [17] by using the hypervirial relations [18,19,20] and the Padé approximant method. The bound-state energies of the ECSC potential for all eigenstates were accurately determined within the framework of the hypervirial Padé scheme [21].…”

Section: Introductionmentioning

confidence: 99%