DKP Oscillator in a Noncommutative Space

Abstract

We present the DKP oscillator model of spins 0 and 1, in a noncommutative space. In the case of spin 0, the equation is reduced to Klein-Gordon oscillator type, the wave functions are then deduced and compared with the DKP spinless particle subjected to the interaction of a constant magnetic field. For the case of spin 1, the problem is equivalent with the behavior of the DKP equation of spin 1 in a commutative space describing the movement of a vectorial boson subjected to the action of a constant magnetic field with additional correction which depends on the noncommutativity parameter.

DKP Oscillator with Spin-0 in Three-dimensional Noncommutative Phase Space

“…Making use of the solution of component ψ 1 (ρ, φ, x 3 ) and considering (15), finally the corresponding total wave function ψ(ρ, φ, x 3 ) can be deduced. As a consequence, the total wave function ψ(ρ, φ, x 3 ) can be expressed…”

“…This was initially motivated by studies of the low energy effective theory of D-brane with a nonzero Neveu-Schwarz B field background. Many efforts have been devoted to the various aspects of noncommutative quantum mechanics, such as Quantum Hall effect [10,14], Landau problem on noncommutative plane [1,11,16], the two-dimensional quantum system with arbitrary central potential [2,17], and the DKP oscillator in a noncommutative space [15], etc. The noncommutative phase space is characterized by the fact that their coordinate operators satisfy the equation [4],…”

“…The goal of this study is to find the exact wave functions and the energy levels of DKP equation with Dirac oscillator potential for spin-0 particles [15,27,29] in noncommutative phase space.…”

Quantum dynamics of scalar bosons in a cosmic string background

“…The name distinguishes it from the system called a DKP oscillator with Lorentz tensor couplings of Ref. [10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25].…”

Relativistic Oscillators in a Noncommutative Space: a Path Integral Approach

“…Instead of solving the path integral representation for the two-dimensional Dirac and Klein-Gordon oscillators in a noncommutative space by using the starproduct procedure, we use Bopp's shift [30], which is defined in (13). It is known that the nonrelativistic harmonic oscillator in a noncommutative space has a similar behaviour to the Landau problem in a commutative space [31].…”