GROUP THEORETICAL INTERPRETATION OF VON-NEUMANNS THEOREM ON COMPOSITE SYSTEMS

We show that the physical meaning of a mathematical theorem on composite systems (described quantum mechanically) established by von Neumann becomes transparent with reference to a physical example, i.e., that of a composite system in a state of definite angular momentum. In this case the theorem is shown to reproduce the Clebsch-Gordan expansion, a fact which has been universally ignored. The theorem has a more general validity, the only condition being the existence of a conservation law, or, in other terms, of an underlying group structure (at least for cases of physical interest). This circumstance, in the case of non-Abelian groups, proves essential in the discussion of the Einstein, Podolsky, Rosen paradox and related problems. © 1979, American Association of Physics Teachers. All rights reserved.