Relativistic Dynamics of a Quantum System

In this paper, we examine quantum systems with relativistic dynamics. We show that for a successful description of these systems, the application of Galilei invariant nonrelativistic Hamiltonian is necessary. To modify this Hamiltonian to relativistic dynamics, we require precise relativistic kinetic energy operators instead of nonrelativistic ones for every internal (Jacobi) coordinate. Finally, we introduce and investigate the Schru0026oumldinger equation with relativistic dynamics for two-particle systems with harmonic oscillator and Coulomb potentials.