Chin. Phys. Lett.  2015, Vol. 32 Issue (10): 100302    DOI: 10.1088/0256-307X/32/10/100302
GENERAL |
Motion of a Nonrelativistic Quantum Particle in Non-commutative Phase Space
FATEME Hoseini1**, MA Kai2 , HASSAN Hassanabadi1
1Physics Department, University of Shahrood, Shahrood 3619995161-316, Iran
2School of Physics Science, Shaanxi University of Technology, Hanzhong 723000
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FATEME Hoseini, MA Kai, HASSAN Hassanabadi 2015 Chin. Phys. Lett. 32 100302
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Abstract The equation governing the motion of a quantum particle is considered in nonrelativistic non-commutative phase space. For this aim, we first study new Poisson brackets in non-commutative phase space and obtain the modified equations of motion. Next, using novel transformations, we solve the equation of motion and report the exact analytical solutions.
Received: 03 August 2015      Published: 30 October 2015
PACS:  03.65.-w (Quantum mechanics)  
  03.65.Db (Functional analytical methods)  
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https://cpl.iphy.ac.cn/10.1088/0256-307X/32/10/100302       OR      https://cpl.iphy.ac.cn/Y2015/V32/I10/100302
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FATEME Hoseini
MA Kai
HASSAN Hassanabadi
[1] Snyder H S 1947 Phys. Rev. 71 38
[2] Yang C N 1947 Phys. Rev. 72 874
[3] Madore J 1999 An Introduction to Noncommutative Differential Geometry and Its Physical Applications (Cambridge: Cambridge University Press)
[4] Connes A 1985 Inst. Hautes Etudes Sci. Publ. Math. 62 41
[5] Woronowicz S L 1987 Publ. Res. Inst. Math. Sci. 23 117
[6] Akofor E, Balachandran A P and Joseph A 2008 Int. J. Mod. Phys. 23 1637
[7] Grosse H and Wohlgenannt M 2007 Eur. Phys. J. C 52 435
[8] Habara Y 2002 Prog. Theor. Phys. 107 211
[9] Jonke L and Meljanac S 2003 Eur. Phys. J. C 29 433
[10] Zhang J Z 2008 Int. J. Mod. Phys. 23 1393
[11] Li K and Wang J 2007 Eur. Phys. J. C 50 1007
[12] Ribeiro L R, Passos E, Furtado C and Nascimento J R 2008 Eur. Phys. J. C 56 597
[13] Arai A 2009 Representations of a Quantum Phase Space with General Degrees of Freedom Mathematical Physics (Preprint Archive 09-122) (in press)
[14] Yang Z H, Long C Y, Qin S J and Long Z W 2010 Int. J. Theor. Phys. 49 644
[15] Dayi O F and Jellal A 2002 J. Math. Phys. 43 4592
[16] Duval C and Horváthy P A 2001 J. Phys. A: Math. Gen. 34 10097
[17] Alvarez P D, Gomis J, Kamimura K and Plyushchay M S 2008 Phys. Lett. B 659 906
[18] Dayi ? F and Kelleyane L T 2002 Mod. Phys. Lett. A 17 1937
[19] Gamboa J, Loewe M, Mendez F and Rojas J C 2001 Mod. Phys. Lett. A 16 2075
[20] Falek M and Merad M 2008 Commun. Theor. Phys. 50 587
[21] Hassanabadi H, Molaee Z and Zarrinkamar S 2014 Adv. High Energy Phys. 2014 459345
[22] Wei G F, Long C Y, Long Z W, Qin S J and Fu Q 2008 Chin. Phys. C 32 338
[23] Romero J M, Santiago J A and Vergara J D 2003 Phys. Lett. A 310 9
[24] Sakurai J J 1994 Modern Quantum Mechanics (Los Angeles: Late University of California)
[25] Chang Z, Chen W, Guo H Y and Yan H 1991 J. Phys. A 24 1427
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