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 modif...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 Schrödinger equation with relativistic dynamics for two-particle systems with harmonic oscillator and Coulomb potentials.展开更多
An investigation of origins of the quantum mechanical momentum operator has shown that it corresponds to the nonrelativistic momentum of classical special relativity theory rather than the relativistic one, as has bee...An investigation of origins of the quantum mechanical momentum operator has shown that it corresponds to the nonrelativistic momentum of classical special relativity theory rather than the relativistic one, as has been unconditionally believed in traditional relativistic quantum mechanics until now. Taking this correspondence into account, relativistic momentum and energy operators are defined. Schrödinger equations with relativistic kinematics are introduced and investigated for a free particle and a particle trapped in the deep potential well.展开更多
文摘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 Schrödinger equation with relativistic dynamics for two-particle systems with harmonic oscillator and Coulomb potentials.
文摘An investigation of origins of the quantum mechanical momentum operator has shown that it corresponds to the nonrelativistic momentum of classical special relativity theory rather than the relativistic one, as has been unconditionally believed in traditional relativistic quantum mechanics until now. Taking this correspondence into account, relativistic momentum and energy operators are defined. Schrödinger equations with relativistic kinematics are introduced and investigated for a free particle and a particle trapped in the deep potential well.
