The Analytic Eigenvalue Structure of the 1+1 Dirac Oscillator
Quantum Physics
2020-09-02 v3
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.
Keywords
Cite
@article{arxiv.1908.09352,
title = {The Analytic Eigenvalue Structure of the 1+1 Dirac Oscillator},
author = {Bo-Xing Cao and Fu-Lin Zhang},
journal= {arXiv preprint arXiv:1908.09352},
year = {2020}
}
Comments
5.3 pages, 3 figures