Relativistic oscillators in new type of the extended uncertainty principle

Abstract

We present the exact solutions of one-dimensional Klein–Gordon and Dirac oscillators subject to the uniform electric field in the context of the new type of the extended uncertainty principle using the displacement operator method. The energy eigenvalues and eigenfunctions are determined for both cases. For the Klein–Gordon oscillator case, the wave functions are expressed in terms of the associated Laguerre polynomials and for the Dirac oscillator case, the wave functions are obtained in terms of the confluent Heun functions. The limiting cases are also studied using the special values of the physical parameters.

Squeezed coherent states for gravitational well in noncommutative space

“…Instead of building a larger collider, the energy limitation problem can be overcome with the help of performing passive experiments using interferometry. Numerous proposals are there in this regime [19,20,21,22,23,24,25,26,27,28]. However, to the best of knowledge of present authors, none of them had yet been carried out.…”

Supersymmetric quantum mechanics and coherent states for a deformed oscillator with position-dependent effective mass

“…[51][52][53] One of these formulations is derived from a a) Electronic mail: bruno.costa@ifsertao-pe.edu.br b) Electronic mail: cardoso.genilson@outlook.com c) Electronic mail: ignacio.sebastian@ufba.br translation operator that causes non-additive displacements of the type Tγ (ε)|x = |x + (1 + γx)ε , being γ a deformation parameter with inverse length dimension. [54][55][56][57][58][59][60][61][62][63][64][65][66][67] This translation operator leads to a position-dependent linear momentum operator pγ that generates non-additive translations. Consequently, the particle mass is a function of the position controlled by the parameter γ.…”

“…In the displacement-operator formalism, the time-independent Schrödinger equation can be expressed using a deformed derivative operator D γ = (1 + γx)d/dx, which results physically equivalent to introduce a particle with a PDM. Typical problems of quantum mechanics have been solved within this approach: infinite and finite square potential wells, [54][55][56] quantum dots and wells, 57,58 quasiperiodic 59 and Coulomb-like potentials, 60 harmonic oscillator, [61][62][63][64][65] Dirac fermions in graphene 66 and two dimensional electron gas. 67 It can be shown that the energy spectrum of the deformed harmonic oscillator corresponds to the Morse oscillator, i.e., an anharmonic oscillator.…”

Deformed classical-quantum mechanics transition

“…Along the lines outlined previously, much work has been done either modifying the Heisenberg uncertainty relations [1][2][3][4], restudying the classical-quantum mechanics transition [23][24][25][26][27], modifying quantum mechanics using quantum groups [28] or using arguments from noncommutative geometry [29][30][31][32][33][34][35][36][37][38][39][40][41][42] and related arguments [3,[43][44][45][46].…”