Abstract
In this work, the generalized Dirac oscillator in cosmic string space-time is studied by replacing the momentum pμ with its alternative pμ+mωβfμxμ. In particular, the quantum dynamics is considered for the function fμxμ to be taken as Cornell potential, exponential-type potential, and singular potential. For Cornell potential and exponential-type potential, the corresponding radial equations can be mapped into the confluent hypergeometric equation and hypergeometric equation separately. The corresponding eigenfunctions can be represented as confluent hypergeometric function and hypergeometric function. The equations satisfied by the exact energy spectrum have been found. For singular potential, the wave function and energy eigenvalue are given exactly by power series method.
Highlights
Lin-Fang Deng1), Chao-Yun Long1,2)†, Zheng-Wen Long1) and Ting Xu1) 1)Department of Physics, Guizhou University, Guiyang 550025, China 2) Laboratory for Photoelectric Technology and Application, Guizhou University, Guiyang 550025, China Abstract: In this work, the generalized Dirac oscillator in cosmic string space-time is studied by replacing the momentum pμwith its alternative pμ + mωβfμ(xμ)
We look for an exact solution of (27) via the following ansatz to the radial wave function[72,73,74]
The above results show that the radial equation ofthe generalized Dirac oscillator with interaction function fμ(xμ) to be taken as the exponential-type potential can be mapped into the well-known hypergeometric equation and the analytical solutions can have been found
Summary
In cosmic string space–time, the general form of the cosmic string metric in cylindrical coordinates read [41,42,44,58,59]. In this work, we only consider the radial component the non-minimal substitution fμ(xμ) = (0, fρ(ρ), 0,0) By introducing this new coupling (6) into the equation(2) and with the help of the equation(4), in cosmic string space-time the eigenvalue equation of generalized Dirac oscillator can be written as. Ξτ1⁄2 for ξ → 0 andχ ∝ e−2ξ for ξ → ∞, physical solutions χ can be expressed as [44,60,63] If we insert this wave function χ into Eq(20), we have the second-order homogeneous linear differential equation in the following form: d2g dξ. In order to obtain solution forf(ρ) being exponential-type potential, we firstly consider the following linear second-order differential equation x2(1. We will use the results given here to obtain the solutions of Dirac equation exponential-type interaction in cosmic string space-time.
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