Abstract
The generalized Dirac oscillator as one of the exact solvable models 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 sixth 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.
Highlights
IntroductionDirac oscillator is a concept which was first proposed by M
As we all know, Dirac oscillator is a concept which was first proposed by M
In order to describe the complex interactions, Dutta and his colleagues [4] proposed a new concept which is called the generalized Dirac oscillator. It could generalize the linear effect between coordinates and momentum to nonlinear effect by using this system; that is to say, the Dirac oscillator could be regarded as a special case in the generalized Dirac oscillator
Summary
Dirac oscillator is a concept which was first proposed by M. In order to describe the complex interactions, Dutta and his colleagues [4] proposed a new concept which is called the generalized Dirac oscillator. To solve 1+1-dimensional Dirac equation with complex interaction potential, Dutta and colleagues constructed the generalized Dirac oscillator by making a simple transformation p → p − iβf(x). The corresponding complete solutions of 2+1-dimensional radial Dirac equation can be given by the Bethe ansatz method [26,27,28,29] provided that there is appropriate selection of the interactions. The exact solution of this system will be further discussed by using the Bethe ansatz method
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