Research ArticleOpen AccessGoogle Scholar indexed
Noncommutative Phase Space and the Two Dimensional Quantum Dipole in Background Electric and Magnetic Fields
Unité de Recherche en Physique Théorique (URPT), Institut de Mathématiques et de Sciences Physiques (IMSP), Porto-Novo, Bénin
Unité de Recherche en Physique Théorique (URPT), Institut de Mathématiques et de Sciences Physiques (IMSP), Porto-Novo, Bénin
- 1 Unité de Recherche en Physique Théorique (URPT), Institut de Mathématiques et de Sciences Physiques (IMSP), Porto-Novo, Bénin
- 2 Unité de Recherche en Physique Théorique (URPT), Institut de Mathématiques et de Sciences Physiques (IMSP), Porto-Novo, Bénin
Journal of Modern Physics·Volume 04 (2013)·Pages 1400–1411·Published 17 October 2013·DOI10.4236/jmp.2013.410168
Copy link · social · email
Abstract
The two dimensional quantum dipole spring s 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.
KeywordsNoncommutative (NC) Phase SpaceQuantum Dipole<i>su</i>(11) SymmetrySimilarity Transformation
- D. Bahns, S. Doplicher, K. Fredenhagen and G. Piacitelli, Physical Review Letters D, Vol. 71, 2005, pp. 1-12.
- S. Doplicher, K. Fredenhagen and J. E. Roberts, Communications in Mathematical Physics, Vol. 172, 1995, pp. 187-220. http://dx.doi.org/10.1007/BF02104515
- H. Grosse and M. Wohlgenannt, The European Physical Journal, Vol. 52, 2007, pp. 435-450. http://dx.doi.org/10.1140/epjc/s10052-007-0369-5
- Y. Habara, Prog.Theor. Phys, 107, 2002, pp. 211-230. http://dx.doi.org/10.1143/PTP.107.211
- L. Jonke and S. Meljanac, The European Physical Journal C, Vol. 29, 2003, pp. 433-439. http://dx.doi.org/10.1140/epjc/s2003-01205-6
- K. Li and J. Wang, The European Physical Journal C, Vol. 50, 2007, pp. 1007-1011. http://dx.doi.org/10.1140/epjc/s10052-007-0256-0
- 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
- S. Dulat and K. Li, The European Physical Journal C, Vol. 60, 2009, p. 162.
- B. Basu and S. Ghosh, Physics Letters A, Vik, 346, 2005, p. 133.
- F. G. Scholtz, L. Gouba, A. Hafrer, et al., Journal of PhysicsA, Vol. 42, 2009, Article ID: 175303. http://dx.doi.org/10.1088/1751-8113/42/17/175303
- A. Jellal, M. Schreiber and E. H. E. Kinani, International Journal of Modern Physics A, Vol. 20, 2005, p. 1515.
- B. G. Joseph, G. Sunandan and G. S. Frederik, “Harmonic oscillator in a Background Magnetic Field in Noncommutative Quantum Phase-Space,” ICMPA-MPA, 2009.
- X.-M. Yu and K. Li, Chinese Physics Letters, Vol. 25, 2008, p. 1980.
- J. B. Geloun and F. G. Scholtz, Journal of Mathematical Physics, Vol. 50, 2009, Article ID: 043505. http://dx.doi.org/10.1063/1.3105926.3
- F. S. Bemfica and H. O. B. Girotti, Journal of Physics A, Vol. 38, 2008, p. 227.
- Y. Yuan, K. Li, J. H. Wang, et al., Chinese Physics C (HEP and P), Vol. 34, 2010, p. 543. http://dx.doi.org/10.1088/1674-1137/34/5/005
- M.-L. Liang, Y.-B. Zhang, R.-L. Yang and F.-L. Zhang, Chinese Physics C, Vol. 37, 2013, Article ID: 063106. http://dx.doi.org/10.1088/1674-1137/37/6/063106
- X. L. Jiang, C. Long and S. Qin, Journal of Modern Physics, Vol. 4, 2013, pp. 940-944.