The spin–orbit interaction in minimal length quantum mechanics; the case of a (2+1)-dimensional Dirac oscillator

Abstract

We solve the (2+1)-dimensional Dirac oscillator in the presence of spin–orbit interaction within the framework of minimal length quantum mechanics. To report an exact analytical solution, we transform the problem into the momentum space and polar coordinates and thereby obtain the eigenfunctions and eigenenergies of the system.

The Visualization of the Space Probability Distribution for a Moving Particle: In a Single Ring-Shaped Coulomb Potential

“…Since the ring-shaped non-central potentials have potential applications in quantum chemistry and nuclear physics, e.g., they might describe the molecular structure of Benzene and interaction between the deformed nucleuses, it is not surprising that the relevant investigations for them have attracted many attentions [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20]. Based on previous study, we have known that this type of ring-shaped non-central potentials can be solved in spherical coordinates and also the system Hamiltonian with the hidden symmetry makes the bound state energy levels possess an "accidental" degeneracy, which arises from the SU(2) invariance of the Schrödinger Hamiltonian [1].…”