Conversion of the nonrelativistic Schrödinger equation into a class of relativistic equations

Hosung Sun

Frank V. Kowalski

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.

Lawrence Paul Horwitz, F. C. Rotbart

The nonrelativistic limit of a relativistic quantum mechanics of Stueckelberg type is studied. A new degree of freedom, which is a purely quantum effect, emerges as a residue of the relativistic theory; its role is to impose Galilean simultaneity. It is shown that the usual nonrelativistic Schr\"odinger equation is obtained as the asymptotic form of the relativistic evolution equation, and some new insight is provided into its interpretation from the point of view of the relativistic theory.

H. N. Ioannidou

N. I. Ionescu-Pallas