Relativistic particle mechanics and Schrödinger’s quantum wave theory

F. Coaster

S. Rupp

In this paper, some concepts of nonrelativistic many-particle quantum mechanics (e.g., product states, density matrix) are generalized to the relativistic domain using a framework called relativistic Schr\"odinger theory (RST). By using a general ansatz, the RST framework is simplified considerably and some of its field equations are solved directly. The RST approach is then compared with nonrelativistic quantum mechanics (QM) for the case of a product state (conventional QM) and its RST analog. It is shown that relativistic wave equations can be derived from the RST formalism, so that they coincide in the nonrelativistic limit with the well-known Hartree equations.

J. S. Faulkner

Luis Grave de Peralta, Luis A. Poveda, Bill Poirier

Abstract The fundamentals of a quasi-relativistic wave equation, whose solutions match the Schrödinger results for slow-moving particles but are also valid when the particle moves at relativistic speeds, are discussed. This quasi-relativistic wave equation is then used for examining some interesting quantum problems where the introduction of relativistic considerations may produce remarkable consequences. We argue in favor of the academic use of this equation, for introducing students to the implications of the special theory of relativity in introductory quantum mechanics courses.

Erwin K. Kasper

A scalar wave equation is derived which can be applied to the relativistic motion of charged particles in slowly varying electromagnetic fields and which is valid in a sufficiently small energy interval, if spin effects can be neglected. Since this wave equation is a linear partial differential equation of first order in the time derivative but of second order in the space derivatives, it is not relativistically invariant. But it is possible to define a positively definite particle density from which a conservation law can be derived. The main success of this theory is a very simple generalisation of the Schrödinger theory of classical wave mechanics in such a way that it can be also applied to relativistic particles.