Identities and conservation laws in relativistic Schrödinger theory.

K. Greider

Margarete Mattes, M. Sorg

Richard Warren Gurtler, David Hestenes

Properties of observables in the Pauli and Schrödinger theories and first order relativistic approximations to them are derived from the Dirac theory. They are found to be inconsistent with customary interpretations in many respects. For example, failure to identify the ’’Darwin term’’ as the s−state spin−orbit energy in conventional treatments of the hydrogen atom is traced to a failure to distinguish between charge and momentum flow in the theory. Consistency with the Dirac theory is shown to imply that the Schrödinger equation describes not a spinless particle as universally assumed, but a particle in a spin eigenstate. The bearing of spin on the interpretation of the Schrödinger theory is discussed. Conservation laws of the Dirac theory are formulated in terms of relative variables, and used to derive virial theorems and the corresponding conservation laws in the Pauli−Schrödinger theory.

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.

L.D. LANDAU, Efrat Lifshitz

Brian Davies