Motion of a Nonrelativistic Quantum Particle in Non-commutative Phase Space
FATEME Hoseini1** , MA Kai2 , HASSAN Hassanabadi1
1 Physics Department, University of Shahrood, Shahrood 3619995161-316, Iran2 School of Physics Science, Shaanxi University of Technology, Hanzhong 723000
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.
收稿日期: 2015-08-03
出版日期: 2015-10-30
[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
[1]
. [J]. 中国物理快报, 2022, 39(9): 90301-.
[2]
. [J]. 中国物理快报, 2022, 39(4): 47601-.
[3]
. [J]. 中国物理快报, 2022, 39(3): 37302-037302.
[4]
. [J]. 中国物理快报, 2021, 38(6): 60302-.
[5]
. [J]. 中国物理快报, 2021, 38(2): 24202-024202.
[6]
. [J]. 中国物理快报, 2020, 37(12): 120301-.
[7]
. [J]. 中国物理快报, 2020, 37(10): 100301-.
[8]
. [J]. 中国物理快报, 2020, 37(9): 90303-.
[9]
. [J]. 中国物理快报, 2020, 37(8): 89901-.
[10]
. [J]. 中国物理快报, 2019, 36(12): 124701-.
[11]
. [J]. 中国物理快报, 2018, 35(9): 90301-.
[12]
. [J]. 中国物理快报, 2018, 35(5): 50301-.
[13]
. [J]. 中国物理快报, 2018, 35(3): 30202-.
[14]
. [J]. 中国物理快报, 2017, 34(6): 60301-.
[15]
. [J]. 中国物理快报, 2017, 34(5): 50301-.