Noncommutative Phase Space and the Two Dimensional Quantum Dipole in Background Electric and Magnetic Fields


The two dimensional quantum dipole springs in background uniform electric and magnetic fields are first studied in the conventional commutative coordinate space, leading to rigorous results. Then, the model is studied in the framework of the noncommutative (NC) phase space. The NC Hamiltonian and angular momentum do not commute any more in this space. By the means of the su(1,1) symmetry and the similarity transformation, exact solutions are obtained for both the NC angular momentum and the NC Hamiltonian.

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A. Dossa and G. Avossevou, "Noncommutative Phase Space and the Two Dimensional Quantum Dipole in Background Electric and Magnetic Fields," Journal of Modern Physics, Vol. 4 No. 10, 2013, pp. 1400-1411. doi: 10.4236/jmp.2013.410168.

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The authors declare no conflicts of interest.


[1] D. Bahns, S. Doplicher, K. Fredenhagen and G. Piacitelli, Physical Review Letters D, Vol. 71, 2005, pp. 1-12.
[2] S. Doplicher, K. Fredenhagen and J. E. Roberts, Communications in Mathematical Physics, Vol. 172, 1995, pp. 187-220.
[3] H. Grosse and M. Wohlgenannt, The European Physical Journal, Vol. 52, 2007, pp. 435-450.
[4] Y. Habara, Prog.Theor. Phys, 107, 2002, pp. 211-230.
[5] L. Jonke and S. Meljanac, The European Physical Journal C, Vol. 29, 2003, pp. 433-439.
[6] K. Li and J. Wang, The European Physical Journal C, Vol. 50, 2007, pp. 1007-1011.
[7] L. R. Ribeiro, E. Passos, C. Furtado and J. R. Nascimento, The European Physical Journal C, Vol. 56, 2008, pp. 597-606. arXiv: hep-th/0711.1773
[8] S. Dulat and K. Li, The European Physical Journal C, Vol. 60, 2009, p. 162.
[9] B. Basu and S. Ghosh, Physics Letters A, Vik, 346, 2005, p. 133.
[10] F. G. Scholtz, L. Gouba, A. Hafrer, et al., Journal of PhysicsA, Vol. 42, 2009, Article ID: 175303.
[11] A. Jellal, M. Schreiber and E. H. E. Kinani, International Journal of Modern Physics A, Vol. 20, 2005, p. 1515.
[12] B. G. Joseph, G. Sunandan and G. S. Frederik, “Harmonic oscillator in a Background Magnetic Field in Noncommutative Quantum Phase-Space,” ICMPA-MPA, 2009.
[13] X.-M. Yu and K. Li, Chinese Physics Letters, Vol. 25, 2008, p. 1980.
[14] J. B. Geloun and F. G. Scholtz, Journal of Mathematical Physics, Vol. 50, 2009, Article ID: 043505.
[15] F. S. Bemfica and H. O. B. Girotti, Journal of Physics A, Vol. 38, 2008, p. 227.
[16] Y. Yuan, K. Li, J. H. Wang, et al., Chinese Physics C (HEP and P), Vol. 34, 2010, p. 543.
[17] M.-L. Liang, Y.-B. Zhang, R.-L. Yang and F.-L. Zhang, Chinese Physics C, Vol. 37, 2013, Article ID: 063106.
[18] X. L. Jiang, C. Long and S. Qin, Journal of Modern Physics, Vol. 4, 2013, pp. 940-944.
[19] K. Li and S. Dulat, Chin. Phys. C, Vol. 34, 2010.
[20] A. Jago, “Noncommutative Geometry and Supersymmetry in a Generalization of the Bigatti-Susskind System,” Master Thesis, Université Catholique de Louvain, Louvain-La-Neuve, 2011.
[21] D. Bigatti and L. Susskind, Physical Review D, Vol. 62, 2000, Article ID: 066004.
[22] J. Govaerts, M. N. Hounkonnou and H. V. Mweenec, “Variations on the Planar Landau Problem: Canonical Transformations, A Purely Linear Potential and the Half-Plane 2009”. e-print arXiv: 0909.2659v1
[23] A. E. F. Djemai and H. Smail, International Academic Publishers, Vol. 41, 2004, pp. 937-844.
[24] K. Li, J. H. Wang and C. Y. Chen, Modern Physics Letters A, Vol. 20, 2005, p. 2165.
[25] P. Polychronakos, Physics Letters B, Vol. 505, 2001, p. 267.
L. Mezincescu, 2000. arXiv:hep-th/0007046
[26] R. Jackiw, Nuclear Physics B—Proceedings Supplements, Vol. 108, 2002, pp. 30-36.
[27] A. Connes, “Noncommutative Geometry,” Academic Press San Diego, 1994.
[28] N. Seiberg and E. Witten, Journal of High Energy Physics, Vol. 9, 1999, Article ID: 032.
[29] J. Gamboa, M. Loewe, F. Méndez and J. C. Rojas, Modern Physics Letters A, Vol. 16, 2001, p. 2075, E-Preprint arXiv:hep-th/0104224
[30] K. Li, X.-H. Cao and D.-Y. Wang, Chinese Physics, Vol. 15, 2006, pp. 2236-2239.
[31] H. Tütüncüler and R. Koc, Turkish Journal of Physics, Vol. 28, 2004, pp. 145-153.
[32] R. Koc, O. Ozer, H. Tütüncüler and R. G. Yldrm, The European Physical Journal B, Vol. 59, 2007, pp. 375-383.
[33] I. S. Gradshteyn and I. M. Ryzhik, “Table of Integrals, Series, and Products,” 6th Edition, Academic Press, Waltham, 2000.

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