Analytical approximations to the l-wave solutions of the Schrödinger equation with a hyperbolic potential

Shishan Dong; S. G. Miranda; F. M. Enriquez; Shi Hai Dong

doi:10.1142/S0217984908015024

Analytical approximations to the l-wave solutions of the Schrödinger equation with a hyperbolic potential

Shishan Dong, S. G. Miranda, F. M. Enriquez, Shi Hai Dong

Research output: Contribution to journal › Article › peer-review

15 Scopus citations

Abstract

The bound-state solutions of the Schrödinger equation for a hyperbolic potential with the centrifugal term are presented approximately. It is shown that the solutions can be expressed by the hypergeometric function ₂F₁(a, b; c; z). To show the accuracy of our results, we calculate the energy levels numerically for arbitrary quantum numbers n and l. It is found that the results are in good agreement with those obtained by other methods for short-range potential. Two special cases for l = 0 and σ = 1 are also studied briefly.

Original language	English
Pages (from-to)	483-489
Number of pages	7
Journal	Modern Physics Letters B
Volume	22
Issue number	7
DOIs	https://doi.org/10.1142/S0217984908015024
State	Published - 20 Mar 2008

Keywords

Arbitrary l state
Bound states
Hyperbolic potential

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10.1142/S0217984908015024

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title = "Analytical approximations to the l-wave solutions of the Schr{\"o}dinger equation with a hyperbolic potential",

abstract = "The bound-state solutions of the Schr{\"o}dinger equation for a hyperbolic potential with the centrifugal term are presented approximately. It is shown that the solutions can be expressed by the hypergeometric function 2F1(a, b; c; z). To show the accuracy of our results, we calculate the energy levels numerically for arbitrary quantum numbers n and l. It is found that the results are in good agreement with those obtained by other methods for short-range potential. Two special cases for l = 0 and σ = 1 are also studied briefly.",

keywords = "Arbitrary l state, Bound states, Hyperbolic potential",

author = "Shishan Dong and Miranda, {S. G.} and Enriquez, {F. M.} and Dong, {Shi Hai}",

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T1 - Analytical approximations to the l-wave solutions of the Schrödinger equation with a hyperbolic potential

AU - Dong, Shishan

AU - Miranda, S. G.

AU - Enriquez, F. M.

AU - Dong, Shi Hai

PY - 2008/3/20

Y1 - 2008/3/20

N2 - The bound-state solutions of the Schrödinger equation for a hyperbolic potential with the centrifugal term are presented approximately. It is shown that the solutions can be expressed by the hypergeometric function 2F1(a, b; c; z). To show the accuracy of our results, we calculate the energy levels numerically for arbitrary quantum numbers n and l. It is found that the results are in good agreement with those obtained by other methods for short-range potential. Two special cases for l = 0 and σ = 1 are also studied briefly.

AB - The bound-state solutions of the Schrödinger equation for a hyperbolic potential with the centrifugal term are presented approximately. It is shown that the solutions can be expressed by the hypergeometric function 2F1(a, b; c; z). To show the accuracy of our results, we calculate the energy levels numerically for arbitrary quantum numbers n and l. It is found that the results are in good agreement with those obtained by other methods for short-range potential. Two special cases for l = 0 and σ = 1 are also studied briefly.

KW - Arbitrary l state

KW - Bound states

KW - Hyperbolic potential

UR - http://www.scopus.com/inward/record.url?scp=43949089831&partnerID=8YFLogxK

U2 - 10.1142/S0217984908015024

DO - 10.1142/S0217984908015024

M3 - Artículo

SN - 0217-9849

VL - 22

SP - 483

EP - 489

JO - Modern Physics Letters B

JF - Modern Physics Letters B

IS - 7

ER -

Analytical approximations to the l-wave solutions of the Schrödinger equation with a hyperbolic potential

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