An Axiomatic Formulation of Quantum Mechanics

An Axiomatic Formulation of Quantum Mechanics

Abstract

Von Neumann’s axiomatic treatment of non-relativistic quantum mechanics is the 

archetypal example of the dual interaction between physical theories and the devel- 

opment of mathematical ideas. We examine this interaction by first building up the 

necessary parts of the theory of unbounded self-adjoint operators on a Hilbert space, 

emphasizing the physical intuition that motivates the mathematical concepts. We 

then present a version of the Dirac-von Neumann axioms on a quantum system and 

deduce some of their elementary consequences, illustrating the converse effect of the 

mathematical formalism on the physical theory. 

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