A Statistical Derivation of Non-Relativistic Quantum Theory

Abstract

Quantum theory may either be defined by a set of axioms or otherwise be ’derived’ from classical physics by using certain assumptions. Today, QT is frequently identified with a set of axioms defining a Hilbert space structure. This mathematical structure has been created (by von Neumann) by abstraction from the linear solution space of the central equation of QT, the Schrödinger equation. Thus, deriving Schrödinger’s equation is basically the same as deriving QT. To derive the most general version of the time-dependent Schrödinger equation, describing N particles with spin in an external gauge field, means to derive essentially the whole of non-relativistic QT.