Relativistic dynamics of a quantum system

Abstract

In this paper, we examine quantum systems with relativistic dynamics. We show that for a successful description of these systems, the application of Ga-lilei invariant nonrelativistic Hamiltonian is necessary. To modify this Ha-miltonian to relativistic dynamics, we require precise relativistic kinetic ener-gy operators instead of nonrelativistic ones for every internal (Jacobi) coordi-nate. Finally, we introduce and investigate the Schrödinger equation with re-lativistic dynamics for two-particle systems with harmonic oscillator and Coulomb potentials