Generalized relativistic harmonic oscillator in minimal length quantum mechanics
@article{Castro2016GeneralizedRH, title={Generalized relativistic harmonic oscillator in minimal length quantum mechanics}, author={Luis B. Castro and Angel E. Obispo}, journal={arXiv: High Energy Physics - Theory}, year={2016} }
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 fermion 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.
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References
SHOWING 1-10 OF 51 REFERENCES
An exact solution of the one-dimensional Dirac oscillator in the presence of minimal lengths
- Physics
- 2006
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…
Minimal length and generalized Dirac equation
- Physics
- 2005
Existence of a minimal observable length which has been indicated by string theory and quantum gravity, leads to a modification of Dirac equation. In this letter we find this modified Dirac equation…
Relativistic Quantum Mechanics
- Physics
- 1965
In this text the authors develop a propagator theory of Dirac particles, photons, and Klein-Gordon mesons and per- form a series of calculations designed to illustrate various useful techniques and…
Three-Dimensional Dirac Oscillator with Minimal Length: Novel Phenomena for Quantized Energy
- Physics
- 2013
We study quantum features of the Dirac oscillator under the condition that the position and the momentum operators obey generalized commutationrelations that lead to the appearance of minimal length…
Exact solutions of the (2+1) dimensional Dirac equation in a constant magnetic field in the presence of a minimal length
- Physics
- 2013
We study the (2+1) dimensional Dirac equation in an homogeneous magnetic field (relativistic Landau problem) within a minimal length, or generalized uncertainty principle -GUP-, scenario. We derive…
On the Boundary Conditions in Deformed Quantum Mechanics with Minimal Length Uncertainty
- Physics
- 2013
We find the coordinate space wave functions, maximal localization states, and quasiposition wave functions in a GUP framework that implies a minimal length uncertainty using a formally self-adjoint…
Klein Paradox for the Bosonic Equation in the Presence of Minimal Length
- Physics, Mathematics
- 2015
We present an exact solution of the one-dimensional modified Klein Gordon and Duffin Kemmer Petiau (for spins 0 and 1) equations with a step potential in the presence of minimal length in the…
The Dirac oscillator
- Physics
- 1989
Dirac's free particle equation originated in an attempt to express linearly the relativistic quadratic relation between energy and momentum. The authors introduce a Dirac equation which, besides the…
MINIMUM PHYSICAL LENGTH AND THE GENERALIZED UNCERTAINTY PRINCIPLE IN STRING THEORY
- Physics, Mathematics
- 1990