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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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| Cite this article: |
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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 $n=0$.
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Received: 12 May 2020
Published: 01 September 2020
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| PACS: |
03.65.Pm
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(Relativistic wave equations)
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03.65.Ge
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(Solutions of wave equations: bound states)
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03.65.-w
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(Quantum mechanics)
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| Fund: Supported by the National Natural Science Foundation of China (Grant Nos. 11675119, 11575125 and 11105097). |
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