Neumann axioms From Wikipedia, the free encyclopedia Jump to: navigation , search In mathematical physics , the Dirac–von Neumann axioms give a mathematical formulation of quantum mechanics in terms of operators on a Hilbert space . They were introduced by Dirac ( 1930 ) and von Neumann ( 1932 ). Contents [ hide ] 1 Hilbert space formulation 2 Operator algebra formulation 2.1 Example 3 See also 4 References Hilbert space formulation [ edit ] The space H is a fixed complex Hilbert space of countable infinite dimension . The observables of a quantum system are defined to be the (possibly unbounded ) self-adjoint operators A on H . A state φ of the quantum system is a unit vector of H , up to scalar multiples. The expectation value of an observable A for a system in a state φ is given by the inner product (φ, A φ). Operator algebra formulation [ edit ] The Dirac–von Neumann axioms can be f...
