Nontrivial systems and the necessity of the scalar quantum mechanics axioms

Abstract

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.