The Analytic Eigenvalue Structure of the 1+1 Dirac Oscillator
Bo-Xing Cao and Fu-Lin Zhang*
Department of Physics, School of Science, Tianjin University, Tianjin 300072, China
Abstract ：We study the analytic structure for the eigenvalues of the one-dimensional Dirac oscillator, by analytically continuing its frequency on the complex plane. A twofold Riemann surface is found, connecting the two states of a pair of particle and antiparticle. One can, at least in principle, accomplish the transition from a positive energy state to its antiparticle state by moving the frequency continuously on the complex plane, without changing the Hamiltonian after transition. This result provides a visual explanation for the absence of a negative energy state with the quantum number $n=0$.
收稿日期: 2020-05-12
出版日期: 2020-09-01
:
03.65.Pm
(Relativistic wave equations)
03.65.Ge
(Solutions of wave equations: bound states)
03.65.-w
(Quantum mechanics)
[1] Dembowski C, Gräf H D, Heine H L, Heiss W D, Rehfeld H and Richter A 2001 Phys. Rev. Lett. 86 787 [2] Dietz B, Harney H L, Kirillov O N, Miski-Oglu M, Richter A and Schäfer F 2011 Phys. Rev. Lett. 106 150403 [3] Doppler J, Mailybaev A A, Böhm J, Kuhl U, Girschik A, Libisch F, Milburn T J, Rabl P, Moiseyev N and Rotter S 2016 Nature 537 76 [4] Chen W, Özdemir S K, Zhao G, Wiersig J and Yang L 2017 Nature 548 192 [5] Xu H, Mason D, Jiany L and Harris J G E 2016 Nature 537 80 [6] Bender C M, Felski A, Hassanpour N, Klevansky S P and Beygi A 2017 Phys. Scr. 92 015201 [7] Felski A and Kelvansky S P 2018 Phys. Rev. A 98 012127 [8] Bender C M and Turbiner A 1993 Phys. Lett. A 173 442 [9] Moshinsky M and Szczepaniak A 1989 J. Phys. A 22 L817 [10] Sadurní E 2011 AIP Conf. Proc. 1334 249 [11] Dirac P A M 1965 The Principles of Quantum Mechanics (Oxford: Oxford University Press) p 253 [12] Franco-Villafañe J A, Sadurní E, Barkhofen S, Kuhl U, Mortessagne F and Seligman T H 2013 Phys. Rev. Lett. 111 170405 [13] Lange de O L 1991 J. Phys. A 24 667 [14] Benitez J 1990 Phys. Rev. Lett. 64 1643 [15] Quesne C and Moshinsky. M 1990 J. Phys. A 23 2263 [16] Lisboa R, Malheiro M, de Castro A S, Alberto P and Fiolhais M 2004 Phys. Rev. C 69 024319 [17] Zhang F L, Fu B and Chen J L 2009 Phys. Rev. A 80 054102 [18] Grineviciute J and Halderson D 2012 Phys. Rev. C 85 054617 [19] Romera E 2011 Phys. Rev. A 84 052102 [20] Bermudez A, Martin-Delgado M A and Solano E 2007 Phys. Rev. A 76 041801 [21] Bermudez A, Martin-Delgado M A and Solano E 2007 Phys. Rev. Lett. 99 123602 [22] Lamata L, León J, Schätz T and Solano E 2007 Phys. Rev. Lett. 98 253005 [23] Torres J M, Sadurní E and Seligman T H 2010 AIP Conf. Proc. 1323 301 [24] Sadurní E, Seligman T H and Mortessagne F 2010 New J. Phys. 12 053014 [25] Szmytkowski R and Gruchowski M 2001 J. Phys. A 34 4991 [26] Greiner W 2000 Relativistic Quantum Mechanics: Wave Equations (Berlin: Springer) p 299 [27] Bender C M, Brody D C and Jones H F 2003 Am. J. Phys. 71 1095 [28] Beygi A and Klevansky S P 2018 Phys. Rev. A 98 022105 [29] Beygi A, Klevansky S P and Bender C M 2019 Phys. Rev. A 99 062117 [30] Berry M V 1984 Proc. R. Soc. London Ser. A 392 45
[1]
.
[2]
.
[3]
.
[4]
.
[5]
.
[6]
.
[7]
REN Na, WANG Jia-Xiang, LI An-Kang, WANG Ping-Xiao. Pair Production in an Intense Laser Pulse: The Effect of Pulse Length
[8]
HUANG Zeng-Guang**;FANG Wei;;LU Hui-Qing;
. Inflation and Singularity of a Bianchi Type-VII0 Universe with a Dirac Field in the Einstein–Cartan Theory
[9]
HUANG Zeng-Guang**;FANG Wei;LU Hui-Qing;**
. Inflation and Singularity in Einstein–Cartan Theory
[10]
Marina-Aura Dariescu**;Ciprian Dariescu;Ovidiu Buhucianu
. Charged Scalars in Transient Stellar Electromagnetic Fields
[11]
FENG Jun-Sheng**;LIU Zheng;GUO Jian-You
. Bound and Resonant States of the Hulthén Potential Investigated by Using the Complex Scaling Method with the Oscillator Basis
[12]
PAN Qi-Yuan;JING Ji-Liang. Late-Time Evolution of the Phantom Scalar Perturbation in the Background of a Spherically Symmetric Static Black Hole
[13]
S. H. Kim. Identification of the Amplification Mechanism in the First Free-Electron Laser as Net Stimulated Free-Electron Two-Quantum Stark Emission
[14]
S. H. Kim. Electric-Wiggler-Enhanced Three-Quantum Scattering and the Output Power Affected by this Scattering in a Free-Electron Laser
[15]
M. R. Setare;O. Hatami. Exact Solutions of the Dirac Equation for an Electron in a Magnetic Field with Shape Invariant Method
2020, Vol. 37 
