Formulation of Schrödinger-Like Relativistic Wave Equation of Motion

Young‐Sea Huang

Tal Hendel

Abstract The equation of motion in the standard formulation of non-relativistic quantum mechanics, the Schrödinger equation, is based on the Hamiltonian. In contrast, in Feynman’s path-integral formulation of quantum mechanics, the equation of motion is the propagation equation, which is based on the Lagrangian. That these two different equations of motion are equivalent was shown by Feynman, who provided a derivation of the Schrödinger equation from the propagation equation. Surprisingly, however, while in classical mechanics there exists a simple relationship between the Hamiltonian and the Lagrangian, there is nothing in Feynman’s derivation that gives any indication of this relationship. Here I show that the equations of motion in the Hamiltonian and Lagrangian formulations of quantum mechanics are, in fact, simply related to each other.

В. М. Симулик, I.Yu. Krivsky

The foundations of the relativistic canonical quantum mechanics of a fermionic doublet on the basis of the Schrodinger–Foldy equation of motion are formulated. A brief review of the different ways of the Dirac equation derivation is given. The Dirac equation is derived from the Schrodinger–Foldy equation of the relativistic canonical quantum mechanics. It is shown that our model does not need applying of the negative mass concept of the antiparticle.

Leon W. Cohen

We consider the possibility of formulating classical wave prorogation in a quantum mechanical formalism. The classical wave may have dispersion and attenuation. We derive a Schrödinger type equation of motion where the equivalent Hamiltonian is the dispersion relation. We also derive a Heisenberg equation of motion for the cases with and without damping. When there is damping, we show that the Heisenberg equation of motion contains both a commutator and an anticommutator.