Bound state solutions of relativistic particles in a new ring-shaped non-harmonic oscillator potential

Zhang Min-Cang; Wang Zhen-Bang

doi:10.7498/aps.56.3688

Abstract
In this paper, a new ring-shaped non-harmonic oscillator potential is proposed. Under the condition of equal scalar and vector potentials, the exact bound solutions and energy equations of both the Klein-Gordon equation and Dirac equation for this oscillator potential are obtained. It is shown that the angular wave functions of Klein-Gordon equation are given by the hypergeometric functions and the radial wave functions are expressed in terms of the confluent hypergeometric functions or general Laguerre polynomial. The spinner wave functions of the Dirac equation are constructed with the of the Klein-Gordon equation.

Keywords:
ring-shaped non-harmonic oscillator potential /

Klein-Gordon equation /

Dirac equation /

bound state
Authors and contacts
Zhang Min-Cang,

Wang Zhen-Bang

1.
陕西师范大学物理学与信息技术学院，西安 710062
References

Cited By

[1]	Yan Jun. Study of energy stability and perturbation in the Q-ball solutions of Klein-Gordon equation. Acta Physica Sinica, 2013, 62(23): 230301. doi: 10.7498/aps.62.230301
[2]	Zhang Min-Cang. Transmission resonance for a Klein-Gordon particle in one-dimensional Hulthén potential barrier. Acta Physica Sinica, 2009, 58(9): 5961-5964. doi: 10.7498/aps.58.5961
[3]	Zhang Min-Cang. A relativistic non-harmonic oscillator potential and pseudospin symmetry. Acta Physica Sinica, 2009, 58(1): 61-65. doi: 10.7498/aps.58.61
[4]	Zhang Min-Cang. Quesne-like ring-shaped spherical harmonic oscillator potential and pseudospin symmetry. Acta Physica Sinica, 2009, 58(2): 712-716. doi: 10.7498/aps.58.712
[5]	Wei Gao-Feng, Long Chao-Yun, Qin Shui-Jie, Zhang Xin. Analytical approximations to the arbitrary l-wave bound state solutions of the Klein-Gordon equation for the Manning-Rosen potential. Acta Physica Sinica, 2008, 57(11): 6730-6735. doi: 10.7498/aps.57.6730
[6]	Zhang Min-Cang, Wang Zhen-Bang. Bound states of relativistic particles in the second P?schl-Teller potentials. Acta Physica Sinica, 2006, 55(2): 525-528. doi: 10.7498/aps.55.525
[7]	Zhang Min-Cang, Wang Zhen-Bang. Bound state solutions of the Dirac equation with the Makarov potentials. Acta Physica Sinica, 2006, 55(12): 6229-6233. doi: 10.7498/aps.55.6229
[8]	Zhang Min-Cang, Wang Zhen-Bang. Bound states of the Klein-Gordon equation and Dirac equation with the Manning-Rosen scalar and vector potentials. Acta Physica Sinica, 2006, 55(2): 521-524. doi: 10.7498/aps.55.521
[9]	Chen Zi-Dong, Chen Gang. Bound states solutions of the Klein-Gordon equation with Hartmann potential and recursion relations. Acta Physica Sinica, 2005, 54(6): 2524-2527. doi: 10.7498/aps.54.2524
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[11]	Chen Gang. Bound states of relativistic particles in Rosen-Morse potential. Acta Physica Sinica, 2004, 53(3): 684-687. doi: 10.7498/aps.53.684
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[13]	Lu Fa-Lin, Chen Chang-Yuan. Bound states of Klein-Gordon equation for ring-shaped non-spherical harmonic oscillator potentials. Acta Physica Sinica, 2004, 53(6): 1652-1656. doi: 10.7498/aps.53.1652
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[20]	CHEN GANG. BOUND STATES OF KLEIN-GORDON EQUATION AND DIRAC EQUATION FOR SCALAR AND VECTOR P?SCHL-TELLER-TYPE POTENTIALS. Acta Physica Sinica, 2001, 50(9): 1651-1653. doi: 10.7498/aps.50.1651

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Vol. 56, Issue 7 - 2007-04-05

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Bound state solutions of relativistic particles in a new ring-shaped non-harmonic oscillator potential

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Bound state solutions of relativistic particles in a new ring-shaped non-harmonic oscillator potential

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