Model Nonrelativistic Quantum Mechanics. Considerations

Ashot S. Gevorkyan

ANTON Z. CAPRI

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.

Walter T. Grandy

A. J. Davies

The quaternionic generalization of the Dirac equation is investigated. From elementary considerations of unitarity and Lorentz invariance it is demonstrated that potentials with quaternionic parts are not consistent with representation independence. This result leads to the conclusion that either quaternionic quantum mechanics singles out a special class of Dirac representations, or that allowed potentials appearing in the problem have no j or k components. If the latter alternative is the case, consideration of nonrelativistic wave mechanics casts doubt on the existence of simple experimental tests of quaternionic quantum mechanics.