Chin. Phys. Lett.  2020, Vol. 37 Issue (9): 090303    DOI: 10.1088/0256-307X/37/9/090303
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
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Bo-Xing Cao  and Fu-Lin Zhang 2020 Chin. Phys. Lett. 37 090303
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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 $n=0$.
Received: 12 May 2020      Published: 01 September 2020
PACS:  03.65.Pm (Relativistic wave equations)  
  03.65.Ge (Solutions of wave equations: bound states)  
  03.65.-w (Quantum mechanics)  
Fund: Supported by the National Natural Science Foundation of China (Grant Nos. 11675119, 11575125 and 11105097).
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Bo-Xing Cao  and Fu-Lin Zhang
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