## 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.

### MSC:

 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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