Exact Solution of Klein–Gordon and Dirac Equations with Snyder–de Sitter Algebra

Abstract

In this paper, we present the exact solution of the $$(1+1)$$ -dimensional relativistic Klein–Gordon and Dirac equations with linear vector and scalar potentials in the framework of deformed Snyder–de Sitter model. We introduce some changes of variables, we show that a one-dimensional linear potential for the relativistic system in a space deformed can be equivalent to the trigonometric Rosen–Morse potential in a regular space. In both cases, we determine explicitly the energy eigenvalues and their corresponding eigenfunctions expressed in terms of Romonovski polynomials. The limiting cases are analyzed for $$\alpha _{1}$$ and $$\alpha _{2} \rightarrow 0$$ and are compared with those of literature.