Three-Dimensional Klein–gordon Oscillator in a Background Magnetic Field in Noncommutative Phase Space

Abstract

In noncommutative phase space, wave functions and energy spectra are derived for the three-dimensional (3D) Klein–Gordon oscillator in a background magnetic field. The raising and lowering operators for this system are derived from the Heisenberg equations of motion for a 3D nonrelativistic oscillator. The coherent states are obtained as the eigenstates of the lowering operators and it is found that the coherent states are not the minimum uncertainty states due to the noncommutativity of the space. It is also pointed out that in the semiclassical limit, quantum matrix elements give solutions to the semiclassical equations.

Relativistic quantum motion of spin-0 particles under the influence of noninertial effects in the cosmic string spacetime

“…In recent years, several studies have addressed the Klein-Gordon oscillator in quantum systems [49][50][51][52][53][54][55][56][57]. It has a formulation similar to the vector potential in the previous section, so to study its solutions we will use the following change in momentum operator:…”

A relativistic quantum oscillator subject to a Coulomb-type potential induced by effects of the violation of the Lorentz symmetry

“…It was proposed by Bruce and Minning [45] in analogy with the Dirac oscillator [49] and it has attracted interests in studies of noncommutative space [50,51], in noncommutative phase space [52], in Kaluza-Klein theories [53] and in PT -symmetric Hamiltonian [54]. The relativistic oscillator coupling proposed by Bruce and…”

On the Klein–Gordon oscillator subject to a Coulomb-type potential

“…where m is the rest mass of the scalar particle, ω is the angular frequency of the Klein-Gordon oscillator, ρ = x 2 + y 2 andρ is a unit vector in the radial direction. In recent years, the Klein-Gordon oscillator has been investigated in noncommutative space [16,17], in noncommutative phase space [18] and in PT -symmetric Hamiltonian [19].…”