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

Abstract

We consider a two-dimensional Dirac oscillator in the presence of a magnetic field in non-commutative 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.

Algebraic Approach to Exact Solution of the (2 + 1)-Dimensional Dirac Oscillator in the Noncommutative Phase Space

“…Section 3 is devoted to (2) algebraization of Dirac oscillator in the noncommutative phase space. We obtain the energy eigenvalues and the corresponding wave functions through the sl(2) representation and show that our results are in good agreement with the results of [31]. In Section 4, we present the conclusion.…”

“…Similar to [31,41] and by defining = cos , = sin , and 2 = 2 + 2 , it is seen that the (7) transform into…”

“…Boumali and Hassanabadi [31] solved this problem analytically and obtained the exact solutions in terms of the hypergeometric functions. Within the present study, we intend to illustrate the exact solvability of the problem through the sl(2) algebraization [39].…”

“…Therefore for a given , the energy eigenvalue is obtained from (31) and the corresponding unnormalized wave function can be obtained from (6) as…”

“…For quantum systems in noncommutative space, it is seen that assuming the noncommutativity may be a result of quantum gravity effects, also it is a fruitful theoretical laboratory where we can get some insight on the consequences of noncommutativity in field theory by using standard calculation techniques of quantum mechanics. The study on Dirac equation in noncommutative phase space has also attracted much attention in recent years [25][26][27][28][29][30][31]. For example, study on the relativistic Landau levels of Dirac equation in (2 + 1)-dimensional noncommutative phase space has been shown in [28] and one can see an exact mapping of this relativistic model to the AJC model.…”