An exact solution of the one-dimensional Dirac oscillator in the presence of minimal lengths. (English) Zbl 1091.81017

Summary: Using the momentum space representation, we determine the energy eigenvalues, eigenfunctions and the high-temperature thermodynamic properties of the Dirac oscillator in one dimension in the presence of a minimal length given by \((\Delta X)_{\min}=\hbar \sqrt{\beta}\), where \(\beta\) is the deformation parameter of the modified commutation relation \([X, P] = i\hbar (1 + \beta P^{2})\). The obtained results suggest that the effect of the minimal length could be detected in ultrarelativistic heavy-ion collisions.


81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics
81U15 Exactly and quasi-solvable systems arising in quantum theory
81V35 Nuclear physics
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