Exact solution to two-dimensional isotropic charged harmonic oscillator in uniform magnetic field in non-commutative phase space

WEI Gao-Feng; LONG Chao-Yun; LONG Zheng-Wen; QIN Shui-Jie

doi:10.1088/1674-1137/32/4/001

Chinese Physics C> 2008, Vol. 32> Issue(4) : 247-250 DOI: 10.1088/1674-1137/32/4/001

Exact solution to two-dimensional isotropic charged harmonic oscillator in uniform magnetic field in non-commutative phase space

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Abstract：
In this paper, the isotropic charged harmonic oscillator in uniform magnetic field is researched in the non-commutative phase space; the corresponding exact energy is obtained, and the analytic eigenfunction is presented in terms of the confluent hypergeometric function. It is shown that in the non-commutative space，the isotropic charged harmonic oscillator in uniform magnetic field has the similar behaviors to the Landau problem.

References

[1]

. LI K, WANG J H, CHEN C Y. Modern Physics Letter A,2005, 20: 342. Connes A, Douglas M R, Schwarz A. JHEP, 1998, 9802:003. hep-th/97111623. Douglas M R, Hull C M. JHEP, 1998, 9802: 008. hep-th/97111654. Ardalan F, Arfaei H, Sheikh-Jabbari M M. JHEP, 1999,9902: 16. hep-th/98100725. Seiberg N, Witten E. JHEP, 1999, 9909: 032. hep-th/99081426. CHU C S, Ho P M. Nucl. Phys. B, 1999, 550: 151.hep/98122197. CHU C S, Ho P M. Nucl. Phys. B, 2000, 568: 447.hep/99061928. Ardalan F, Arfaei H, Sheikh-Jabbari M M. Nucl. Phys. B,2000, 576: 578. hep/99061919. Ezawa Z F. Quantum Hall Effects: Field Theoretical Approach and Related Topics. Singapore: World Scientific,200010. Minwalla S, Raamsdonk M V, Seiberg N. JHEP, 2000,0002: 020. hep-th/991207211. Chaichain M, Sheikh-Jabbari M M, Tureanu A. Phys. Rev.Lett., 2001, 86: 271612. Bellucci S, Nersessian A, Sochichiu C. Phys. Lett. B, 2001,522: 34513. Bertolami O, Rosa J G. Phys. Rev. D, 2005, 72: 02501014. Muthukumar B, Mitra P. Phys. Rev. D, 2002, 66: 02770115. LI K, CAO X H, WANG D Y. Chin. Phys., 2006, 15: 223616. ZENG J Y. Quantum Mechanics. Volume Ⅰ. Beijing: Science Press, 1997. 326-32917. Bertolami O, Rosa J G. Phys. Rev. D, 2005, 72: 025010

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WEI Gao-Feng, LONG Chao-Yun, LONG Zheng-Wen and QIN Shui-Jie. Exact solution to two-dimensional isotropic charged harmonic oscillator in uniform magnetic field in non-commutative phase space[J]. Chinese Physics C, 2008, 32(4): 247-250. doi: 10.1088/1674-1137/32/4/001

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Received: 2007-06-19
Revised: 2007-09-10

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通讯作者: 陈斌, bchen63@163.com

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沈阳化工大学材料科学与工程学院沈阳 110142

Exact solution to two-dimensional isotropic charged harmonic oscillator in uniform magnetic field in non-commutative phase space

Corresponding author: WEI Gao-Feng,

Received Date: 2007-06-19

Accepted Date: 2007-09-10

Available Online: 2008-04-05

Abstract:

In this paper, the isotropic charged harmonic oscillator in uniform magnetic field is researched in the non-commutative phase space; the corresponding exact energy is obtained, and the analytic eigenfunction is presented in terms of the confluent hypergeometric function. It is shown that in the non-commutative space，the isotropic charged harmonic oscillator in uniform magnetic field has the similar behaviors to the Landau problem.

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Exact solution to two-dimensional isotropic charged harmonic oscillator in uniform magnetic field in non-commutative phase space

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