Duffin–Kemmer–Petiau oscillator with Snyder-de Sitter algebra

Abstract

We present an exact solution of the one-dimensional Bosonic oscillator for spin 1 and spin 0 particles with the Snyder-de Sitter model, where the energy eigenvalues and eigenfunctions are determined for both cases. The wave functions can be given in terms of Gegenbauer polynomials. We also comment on the thermodynamic properties of the system.

Generalized Dirac Oscillator in Cosmic String Space-Time

“…Where ℒ 1 = λ 2 β 2 + m 2 + k 2 − E 2 , It is easy to see that the differential equation (60) is also similar to the equation (37).…”

“…Comparing equation (47)with (37) and using the results given in the equation (41) and (42),it is not difficult to find the equation obeyed byeigenvalues and eigenfunctions and they can be given respectively In this section, we we are interested in considering the Hulthé n potential that describe the interaction between two atoms and has been used in different areas of physics and attracted a great of interest for some decades [81,82,93]. Next we take the interaction function f(ρ) being Hulthé n-Type potential…”

“…oscillator has many applications and has been studied extensively in different field ssuch as high energy physics [12][13][14][15],condensed matter physics [16][17][18], quantum Optics [19][20][21][22][23][24][25] and mathematical physics [26][27][28][29][30][31][32][33] etc. On the other hand, the analysis of gravitational interactions with a quantum mechanical system has recently attracted a great deal attention and has been an active field of research [5][6][34][35][36][37][38][39][40][41][42][43].The study of quantum mechanical problems in curved space-time can be considered as a new kind of interaction between quantum matter and gravitation in the microparticle world. In recent years, the Dirac oscillator embedded in a cosmic string background has inspired a great deal of research such as the dynamics of Diracoscillator in the space -time of cosmic string [44][45][46][47], Aharonov-Casher effect on the Dirac oscillator [5,48], noninertial effects onthe Dirac oscillator in the cosmic string space-time [49]…”

Graphene in curved Snyder space

“…The SdS phase space can be realized in 6-dimensional space as SO (1, 5 [25]. Recently, many authors have condensed their studies on the discussions over the deformed canonical commutation relations [25][26][27][28][29][30][31][32][33][34][35][36][37].…”

2D Relativistic Oscillators with a Uniform Magnetic Field in Anti-deSitter Space

“…We also mention the thermodynamic quantities for a linear potential for Klein-Gordon (KG) and Dirac equations [18] and for a one-dimensional Schrödinger equation with a harmonic oscillator plus an inverse square potential [19]. Some aspects of the bosonic oscillator has also been studied in a thermal bath in deformed quantum mechanics [20][21][22].…”