Generalized relativistic harmonic oscillator in minimal length quantum mechanics

Abstract

Abstract. 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.

On the Relativistic Harmonic Oscillator

“…Using Equations ( 28) and ( 7), one expands Equation (11) in powers of μ 2 , and solves for the higher-order corrections in Equation ( 28). The boundary conditions for all F 2n are:…”

“…Figure 14 presents a comparison between the β dependence of the Fourier coefficients of η'(θ), obtained from the numerical solution of Equation (11), and the spectrum of Equation (35). There is a qualitative difference between the β-dependence of the Fourier coefficients for small β and the spectrum of the asymptotic step-function profile.…”

“…In Figure 15, a comparison between the Fourier coefficients of η'(θ), computed 28) and ( 32) and from numerical solution of Equation (11). μ = 0.2.…”

Quantum Cycle in Relativistic Non-Commutative Space with Generalized Uncertainty Principle correction

“…So, for this working medium with relativistic and GUP correction, we encounter a catalytic effect in the efficiency of the cycle with the increase of the NC parameter. The range of the NC parameter is considered in such a way that it does not exceed the extreme quantum gravity limit [53]. Though it seems like that the efficiency of the engine is monotonously increasing with the NC parameter, there is a bound on it due to the accessible range of the NC parameter.…”

Analysis of the Dirac equation with the Killingbeck potential in non-commutative space

“…As one solvable model, there are many ways to study, including: Nikiforov-Uvarov (NU) method [7][8][9], the asymptotic iteration method (AIM) [10,11] and supersymmetry quantum mechanics (SUSYQM) [12]. If doing momentum transformation, it is well-known as Dirac oscillator [13], which is a typical system investigated in the curved space [14][15][16][17][18], and the effect of generalized uncertainty principle on spin- 1 2 Dirac oscillator and spin-0 or 1 DKP oscillator also are addressed [19][20][21]. Noncommutativity is an interesting topic whatever in mathematics and physics.…”