A relativistic non-harmonic oscillator potential and pseudospin symmetry

Zhang Min-Cang

doi:10.7498/aps.58.61

Abstract
A generalized non-harmonic oscillator potential for spin 1/2 particles is studied. The Dirac Hamiltonian contains a scalar and a vector non-harmonic oscillator potentials. Setting either or both combinations Σ(r)=S(r)+V(r) and Δ(r)=V(r)-S(r) to zero, analytical solutions for bound states of the corresponding Dirac equation are found. The eigenenergies and wave functions are presented, showing the pseudospin symmetry exists exactly.The relations between radial nodes of upper and lower components of the Dirac spinor are obtained.

Keywords:
non-harmonic oscillator potential /

Dirac equation /

pseudospin symmetry /

bound state
Authors and contacts
Zhang Min-Cang

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

Cited By

[1]	Gao Jie, Zhang Min-Cang. Tridiagonal representation with pseudospin symmetry for a noncentral electric dipole and a ring-shaped anharmonic oscillator potential. Acta Physica Sinica, 2016, 65(2): 020301. doi: 10.7498/aps.65.020301
[2]	Zhang Min-Cang. Pseudospin symmetry for a noncentral electric dipole ring-shaped potential in the tridiagonal representation. Acta Physica Sinica, 2012, 61(24): 240301. doi: 10.7498/aps.61.240301
[3]	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
[4]	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
[5]	Zhang Min-Cang, Wang Zhen-Bang. Bound state solutions of relativistic particles in a new ring-shaped non-harmonic oscillator potential. Acta Physica Sinica, 2007, 56(7): 3688-3692. doi: 10.7498/aps.56.3688
[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 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
[8]	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
[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
[10]	Li Ning, Ju Guo-Xing, Ren Zhong-Zhou. Bound states for a kind of relativistic non-harmonic oscillator systems. Acta Physica Sinica, 2005, 54(6): 2520-2523. doi: 10.7498/aps.54.2520
[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
[12]	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
[13]	Chen Gang. Bound states for Dirac equation with Wood-Saxon potential. Acta Physica Sinica, 2004, 53(3): 680-683. doi: 10.7498/aps.53.680
[14]	Zhang Jing-Yi. Entropy of Dirac field in a general spherically symmetric and charged evaporatin g black hole. Acta Physica Sinica, 2003, 52(9): 2354-2358. doi: 10.7498/aps.52.2354
[15]	Chen Chang-Yuan, Liu Cheng-Lin, Lu Fa-Lin, Sun Dong-Sheng. Bound states of the Klein-Gordon equation with n-dimensional scalar and vect or hydrogen atom-type potentials. Acta Physica Sinica, 2003, 52(7): 1579-1584. doi: 10.7498/aps.52.1579
[16]	Chen Gang, Lou Zhi-Mei. Bound states of relativistic particles in a potential with four parameters for d iatomic molecules. Acta Physica Sinica, 2003, 52(5): 1075-1078. doi: 10.7498/aps.52.1075
[17]	Chen Gang, Lou Zhi-Mei. Bound states of relativistic particles in reflectionless-type potential. Acta Physica Sinica, 2003, 52(5): 1071-1074. doi: 10.7498/aps.52.1071
[18]	Guo Jian-You. . Acta Physica Sinica, 2002, 51(7): 1453-1457. doi: 10.7498/aps.51.1453
[19]	Ran Yang-Qiang, Xue Li-Hui, Hu Si-Zhu. . Acta Physica Sinica, 2002, 51(11): 2435-2439. doi: 10.7498/aps.51.2435
[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. 58, Issue 1 - 2009-01-05

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A relativistic non-harmonic oscillator potential and pseudospin symmetry

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A relativistic non-harmonic oscillator potential and pseudospin symmetry

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