Axioms for nonrelativistic quantum mechanics

Neal Zierler

Jan Kotůlek

We discuss the necessity of the axioms of scalar quantum mechanics introduced by Paschke and clearly demonstrate their geometric and/or physical meaning. We show that reasonable nonrelativistic quantum mechanics is exactly specified by the axioms. A system describing the electric Aharonov–Bohm effect is presented. It illustrates the topological obstructions for the existence of a Hamiltonian.

Daniel Rohrlich

The axioms of nonrelativistic quantum mechanics lack clear physical meaning. In particular, they say nothing about nonlocality. Yet quantum mechanics is not only nonlocal, it is twice nonlocal: there are nonlocal quantum correlations, and there is the Aharonov-Bohm effect, which implies that an electric or magnetic field h e r e may act on an electron t h e r e. Can we invert the logical hierarchy? That is, can we adopt nonlocality as an axiom for quantum mechanics and derive quantum mechanics from this axiom and an additional axiom of causality? Three versions of these two axioms lead to three different theories, characterized by "maximal nonlocal correlations", "jamming" and "modular energy". Where is quantum mechanics in these theories?

Santiago Esteban Perez Bergliaffa, H. Vucetich, Gustavo Esteban Romero

Skiff N. Sokolov

A two-dimensional model of relativistic quantum mechanics is suggested which permits any number of particles and a wide class of potentials and is as general as the two-dimensional nonrelativistic quantum mechanics. This proposed model is an example of the application of given axioms. (JFP)

ANTON Z. CAPRI