Minimal Length Quantum Mechanics of Dirac Particles in Noncommutative Space

Abstract

We study the two-dimensional harmonic oscillator in commutative and noncommutative space within the framework of minimal length quantum mechanics for spin-1/2 particles. The energy spectra and the eigenfunction are obtained in both cases. Special cases are also deduced.

Exact solution of the generalized Kemmer oscillator

“…Obviously, equation ( 15) has the same form with the basic equation of the NU method. [37][38][39][40][41][42][43][44][45][46][47] So, it is straight-forward to gain the eigenenergy and the corresponding eigenfunction by using the NU method. By comparing Eq.…”

“…In Eq. ( 18), for the parameter c 3 = 0, the wave function will become into the form as follows: [37][38][39][40][41][42][43][44][45][46][47] ψ 2 (s) = Ns c 12 e c 13 s L c 10 −1…”

“…Then we will derive a complete solution of the generalized Kemmer oscillator within appro-priate choices of the interactions f (x) by using the Nikiforov-Uvarov method. [37][38][39][40][41][42][43][44][45][46][47] This paper is organized as follows.…”

Analysis of nonrelativistic particles in noncommutative phase-space under new scalar and vector interaction terms

“…The two-dimensional harmonic oscillator in commutative and noncommutative spaces within the framework of minimal length quantum mechanics has been investigated by Ikot et al in Ref. [22]. The noncommutative (2+1)-dimensional Duffin-Kemmer-Petiau oscillator under a magnetic field in minimal length formalism is studied in Ref.…”

Solution of the spin-one DKP oscillator under an external magnetic field in noncommutative space with minimal length

“…[25] The minimal length uncertainty relation is another appealing case of the research, in connection with which various topics have been studied. [26][27][28][29][30] Motivated by the intense interest in the study of the minimal length uncertainty relation combination with the noncommutative coordinate space commutation relations in nonrelativistic wave equation and relativistic wave equation, [31][32][33] we study the DKP oscillator for spin-one particle under a magnetic field in the presence of a minimal length in the noncommutative coordinate space in the present work.…”