The exact solutions of a (2 + 1)-dimensional Dirac oscillator under a magnetic field in the presence of a minimal length

Abstract

We consider a two-dimensional Dirac oscillator in the presence of magnetic field in noncommutative phase space in the framework of relativistic quantum mechanics with minimal length. The problem in question is identified with a Poschl-Teller potential. The eigenvalues are found and the corresponding wave functions are calculated in terms of hypergeometric functions.

Exact Solutions of the (2+1)-Dimensional Dirac Oscillator under a Magnetic Field in the Presence of a Minimal Length in the Non-commutative Phase Space

“…By these, the problem in question is identified with a Poschl-Teller potential. Also, when θ and θ ̅ tend to zero, we recover exactly the same results of [43].…”

The Statistical Properties of theq-Deformed Dirac Oscillator in One and Two Dimensions

“…The electromagnetic potential associated with the DO has been found by Benitez et al [21]. The DO has attracted a lot of interests both because it provides one of the examples of the Dirac's equation exact solvability and because of its numerous physical applications [22][23][24][25][26][27]. Finally, Franco-Villafañe et al [28] have exposed the proposal of the first experimental microwave realization of the one-dimensional DO.…”

(2+1)-Dimensional Duffin-Kemmer-Petiau Oscillator under a Magnetic Field in the Presence of a Minimal Length in the Noncommutative Space

“…The interest in the study of the minimal length uncertainty relation combination with the noncommutative space commutation relations in nonrelativistic wave equation and relativistic wave equation has drawn much attention [1][2] in recent years. Motivated by string theory, loop quantum gravity and quantum geometry [3][4][5][6][7][8][9][10][11][12][13][14][15], the modification of the ordinary uncertainty relation has become an appealing case of research.…”