Dynamical Algebras in the 1+1 Dirac Oscillator and the Jaynes–Cummings Model
Wen-Ya Song, Fu-Lin Zhang**
Department of Physics, School of Science, Tianjin University, Tianjin 300072
Abstract ：We study the algebraic structure of the one-dimensional Dirac oscillator by extending the concept of spin symmetry to a noncommutative case. An $SO(4)$ algebra is found connecting the eigenstates of the Dirac oscillator, in which the two elements of Cartan subalgebra are conserved quantities. Similar results are obtained in the Jaynes–Cummings model.
收稿日期: 2020-02-06
出版日期: 2020-04-25
[1] Dirac P A M 1982 The Principles of Quantum Mechanics (Oxford: Oxford University Press) [2] Zee A 2010 Quantum Field Theory in a Nutshell (Princeton: Princeton University Press) [3] Moshinsky M and Szczepaniak A 1989 J. Phys. A 22 L817 [4] Sadurní E 2010 AIP Conf. Proc. 1334 249 [5] Franco-Villafa ne J A, Sadurní E, Barkhofen S, Kuhl U, Mortessagne F and Seligman T H 2013 Phys. Rev. Lett. 111 170405 [6] Grineviciute J and Halderson D 2012 Phys. Rev. C 85 054617 [7] Romera E 2011 Phys. Rev. A 84 052102 [8] Bermudez A, Martin-Delgado M A and Solano E 2007 Phys. Rev. A 76 041801 [9] Bermudez A, Martin-Delgado M A and Solano E 2007 Phys. Rev. Lett. 99 123602 [10] Lamata L, León J, Schätz T and Solano E 2007 Phys. Rev. Lett. 98 253005 [11] Torres J M, Sadurní E and Seligman T H 2010 AIP Conf. Proc. 1323 301 [12] Sadurní E, Seligman T H and Mortessagne F 2010 New J. Phys. 12 053014 [13] Jaynes E T and Cummings F W 1963 Proc. IEEE 51 89 [14] Greiner W and Müller B 1994 Quantum Mechanics (Symmetries) (New York: Springer) [15] De Lange O L and Raab R E 1991 Operator Methods in Quantum Mechanics (Oxford: Clarendon Press) [16] De Lange O L 1991 J. Phys. A 24 667 [17] Benitez J 1990 Phys. Rev. Lett. 64 1643 [18] Zhou J, Su H Y, Zhang F L, Zhang H B and Chen J L 2018 Chin. Phys. Lett. 35 010302 [19] Ge M L, Kwek L C, Liu Y, Oh C H and Wang X B 2000 Phys. Rev. A 62 052110 [20] Ginocchio J N 2005 Phys. Rep. 414 165 [21] Ginocchio J N 2004 Phys. Rev. C 69 034318 [22] Ginocchio J N 2005 Phys. Rev. Lett. 95 252501 [23] Zhang F L, Fu B and Chen J L 2008 Phys. Rev. A 78 040101 [24] Zhang F L, Song C and Chen J L 2009 Ann. Phys. 324 173 [25] Zhang F L, Fu B and Chen J L 2009 Phys. Rev. A 80 054102 [26] Chen J L, Liu Y and Ge M L 1998 J. Phys. A 31 6473 [27] Cao B X and Zhang F L 2019 arXiv:1908.09352 [28] Moreno M and Zentella A 1989 J. Phys. A 22 L821 [29] Vedral V 2005 Modern Foundations of Quantum Optics (London: World Scientific Publishing Company) [30] Irish E 2007 Phys. Rev. Lett. 99 173601 [31] Lu H X and Wang X Q 2000 Chin. Phys. 9 568
[1]
.
[2]
.
[3]
.
[4]
.
[5]
.
[6]
.
[7]
.
[8]
.
[9]
.
[10]
.
[11]
KANG Jing, QU Chang-Zheng. Symmetry Groups and Gauss Kernels of the Schrödinger Equations with Potential Functions
[12]
LIAN Jin-Ling, ZHANG Yuan-Wei, LIANG Jiu-Qing. Macroscopic Quantum States and Quantum Phase Transition in the Dicke Model
[13]
Hassanabadi Hassan1* , Yazarloo Bentol Hoda1 , LU Liang-Liang2 . Approximate Analytical Solutions to the Generalized Pöschl–Teller Potential in D Dimensions
[14]
LIN Bing-Sheng**;HENG Tai-Hua
. Energy Spectra of the Harmonic Oscillator in a Generalized Noncommutative Phase Space of Arbitrary Dimension
[15]
ZHANG Min-Cang**;HUANG-FU Guo-Qing
. Analytical Approximation to the ℓ -Wave Solutions of the Hulthén Potential in Tridiagonal Representation
2020, Vol. 37 
