A Novel Exact Solution of the 2+1-Dimensional Radial Dirac Equation for the Generalized Dirac Oscillator with the Inverse Potentials

Abstract

The generalized Dirac oscillator as one of the exact solvable model in quantum mechanics was introduced in 2+1-dimensional world in this paper. What is more, the general expressions of the exact solutions for these models with the inverse cubic, quartic, quintic and sixtic power potentials in radial Dirac equation were further given by means of the Bethe ansatz method. And finally, the corresponding exact solutions in this paper were further discussed.

Research on the new form of higher-order generalized uncertainty principle in quantum system

“…It is exciting that the Eq. ( 36) could transform into an equation by extracting the appropriate asymptotic behavior, which is formally consistent with the standard equation of the Bethe ansatz method [53][54][55][56][57][58][59][60], and the corresponding exact solution can be derived. In other words, the wave function needs to be transformed as follows…”

Effects of Kaluza-Klein Theory and Potential on a Generalized Klein-Gordon Oscillator in the Cosmic String Space-Time

“…In the literature, f μ ðx μ Þ has chosen similar to potentials encountered in quantum mechanics (Cornell-type, exponential-type, singular, Morse-type, Yukawa-like etc.). A generalized Dirac oscillator in ð2 + 1Þ-dimensional world was studied in [67]. Very recently, the generalized K-G oscillator in the cosmic string space-time in [68] and noninertial effects on a generalized DKP oscillator in the cosmic string space-time in [69] were studied.…”