The energy spectra for Dirac particles in polar coordinates depend on both radial quantum number n ≥ 0 and angular quantum number m ≠ 0 after correcting minor errors in the original derivation.
Exact Mapping of the 2+1 Dirac Oscillator onto the Jaynes-Cummings Model: Ion-Trap Experimental Proposal
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We study the dynamics of the 2+1 Dirac oscillator exactly and find spin oscillations due to a {\it Zitterbewegung} of purely relativistic origin. We find an exact mapping of this quantum-relativistic system onto a Jaynes-Cummings model, describing the interaction of a two-level atom with a quantized single-mode field. This equivalence allows us to map a series of quantum optical phenomena onto the relativistic oscillator, and viceversa. We make a realistic experimental proposal, at reach with current technology, for studying the equivalence of both models using a single trapped ion.
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Comment on "Quantum phase transitions of Dirac particles in a magnetized rotating curved background: Interplay of geometry, magnetization, and thermodynamics"
The energy spectra for Dirac particles in polar coordinates depend on both radial quantum number n ≥ 0 and angular quantum number m ≠ 0 after correcting minor errors in the original derivation.