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Dirac oscillator in perpendicular magnetic and transverse electric fields. (English) Zbl 1360.81148

Summary: We study \((2+1)\) dimensional massless Dirac oscillator in the presence of perpendicular magnetic and transverse electric fields. Exact solutions are obtained and it is shown that there exists a critical magnetic field \(B_c\) such that the spectrum is different in the two regions \(B>B_c\) and \(B<B_c\). The situation is also analyzed for the case \(B=B_c\).

MSC:

81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics
35Q41 Time-dependent Schrödinger equations and Dirac equations
82B27 Critical phenomena in equilibrium statistical mechanics
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