The covariant linear oscillator and generalized realization of the dynamical SU(1,1) symmetry algebra

Abstract

An exactly solvable problem for the finite-difference Schrödinger equation in the relativistic configurational space is considered. The appropriate finite-difference generalization of the factorization method is developed. The theory of new special functions ‘‘the relativistic Hermite polynomials,’’ in which the solutions are expressed, is constructed.