Generalized relativistic harmonic oscillator in minimal length quantum mechanics. (English) Zbl 1370.81069
Summary: We solve the generalized relativistic harmonic oscillator in \(1+1\) dimensions in the presence of a minimal length. Using the momentum space representation, we explore all the possible signs of the potentials and discuss their bound-state solutions for fermions and antifermions. Furthermore, we also find an isolated solution from the Sturm-Liouville scheme. All cases already analyzed in the literature are obtained as particular cases.
MSC:
| 81Q10 | Selfadjoint operator theory in quantum theory, including spectral analysis |
| 81R60 | Noncommutative geometry in quantum theory |
| 70H40 | Relativistic dynamics for problems in Hamiltonian and Lagrangian mechanics |
| 81R20 | Covariant wave equations in quantum theory, relativistic quantum mechanics |
| 34B24 | Sturm-Liouville theory |
| 34L40 | Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) |
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