Analytical approximations to the Schrödinger equation for a second Pöschl-Teller-like potential with centrifugal term

Shi Hai Dong; Wen Chao Qiang; J. García-Ravelo

doi:10.1142/S0217751X0803944X

Analytical approximations to the Schrödinger equation for a second Pöschl-Teller-like potential with centrifugal term

Shi Hai Dong, Wen Chao Qiang, J. García-Ravelo

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58 Scopus citations

Abstract

The bound state solutions of the Schrödinger equation for a second Pöschl-Teller-like potential with the centrifugal term are obtained approximately. It is found that the solutions can be expressed in terms of the hypergeometric functions ₂F₁(a, b; c; z). To show the accuracy of our results, we calculate the eigenvalues numerically for arbitrary quantum numbers n and l. It is found that the results are in good agreement with those obtained by other method for short-range potential. Two special cases for l = 0 and V₁ = V₂ are also studied briefly.

Original language	English
Pages (from-to)	1537-1544
Number of pages	8
Journal	International Journal of Modern Physics A
Volume	23
Issue number	10
DOIs	https://doi.org/10.1142/S0217751X0803944X
State	Published - 20 Apr 2008

Keywords

Bound states
Centrifugal term
Second Pöschl-Teller-like potential

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10.1142/S0217751X0803944X

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title = "Analytical approximations to the Schr{\"o}dinger equation for a second P{\"o}schl-Teller-like potential with centrifugal term",

abstract = "The bound state solutions of the Schr{\"o}dinger equation for a second P{\"o}schl-Teller-like potential with the centrifugal term are obtained approximately. It is found that the solutions can be expressed in terms of the hypergeometric functions 2F1(a, b; c; z). To show the accuracy of our results, we calculate the eigenvalues numerically for arbitrary quantum numbers n and l. It is found that the results are in good agreement with those obtained by other method for short-range potential. Two special cases for l = 0 and V1 = V2 are also studied briefly.",

keywords = "Bound states, Centrifugal term, Second P{\"o}schl-Teller-like potential",

author = "Dong, {Shi Hai} and Qiang, {Wen Chao} and J. Garc{\'i}a-Ravelo",

note = "Funding Information: We would like to thank the kind referee for the invaluable and positive suggestions, which improved the manuscript. This work is supported partly by 20070914-SIP-IPN, COFAA-IPN, Mexico and partly by Natural Science Basic Research Plan in Shaanxi Province of China (Program No. 2005A22), NSF of the Education Bureau of Shaanxi Province of China under Grant O5jk238.",

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AU - Dong, Shi Hai

AU - Qiang, Wen Chao

AU - García-Ravelo, J.

N1 - Funding Information: We would like to thank the kind referee for the invaluable and positive suggestions, which improved the manuscript. This work is supported partly by 20070914-SIP-IPN, COFAA-IPN, Mexico and partly by Natural Science Basic Research Plan in Shaanxi Province of China (Program No. 2005A22), NSF of the Education Bureau of Shaanxi Province of China under Grant O5jk238.

PY - 2008/4/20

Y1 - 2008/4/20

N2 - The bound state solutions of the Schrödinger equation for a second Pöschl-Teller-like potential with the centrifugal term are obtained approximately. It is found that the solutions can be expressed in terms of the hypergeometric functions 2F1(a, b; c; z). To show the accuracy of our results, we calculate the eigenvalues numerically for arbitrary quantum numbers n and l. It is found that the results are in good agreement with those obtained by other method for short-range potential. Two special cases for l = 0 and V1 = V2 are also studied briefly.

AB - The bound state solutions of the Schrödinger equation for a second Pöschl-Teller-like potential with the centrifugal term are obtained approximately. It is found that the solutions can be expressed in terms of the hypergeometric functions 2F1(a, b; c; z). To show the accuracy of our results, we calculate the eigenvalues numerically for arbitrary quantum numbers n and l. It is found that the results are in good agreement with those obtained by other method for short-range potential. Two special cases for l = 0 and V1 = V2 are also studied briefly.

KW - Bound states

KW - Centrifugal term

KW - Second Pöschl-Teller-like potential

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U2 - 10.1142/S0217751X0803944X

DO - 10.1142/S0217751X0803944X

M3 - Artículo

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SP - 1537

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JO - International Journal of Modern Physics A

JF - International Journal of Modern Physics A

IS - 10

ER -

Analytical approximations to the Schrödinger equation for a second Pöschl-Teller-like potential with centrifugal term

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Keywords

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