Consistency in the formulation of the Dirac, Pauli, and Schrödinger theories

Abstract

Properties of observables in the Pauli and Schrödinger theories and first order relativistic approximations to them are d e r i v e d from the Dirac theory. They are found to be i n c o n s i s t e n t 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.