Quantum mechanics leads to irreconcilable contradictions with the classical special theory of relativity (STR). These contradictions are absent if we consider space to be discrete. In this article, the discrete Dirac equation is obtained in the simplest case of one-dimensional discrete space. It is shown that the rejection of the continuous description of space removes the contradictions between the quantum-mechanical description and STR. The possibilities of experimental verification of the theory are considered

one-dimensional Dirac equation, velocity and coordinate operators, Bloch oscillations, anyon

Mathematical modelling in actual problems of science and technics