Mathematical formulation of quantum mechanics

Summary

The mathematical formulation of quantum mechanics describes a physical system by a complex Hilbert space. States are unit vectors or density operators, and measurable quantities are self-adjoint operators. Measurement probabilities come from the spectral theorem through projection-valued measures, and time evolution is a one-parameter unitary group generated by the Hamiltonian. Dirac and von Neumann set out this framework around 1930, and it is also stated as the Dirac–von Neumann axioms. It made quantum theory a part of functional analysis and gave rise to operator algebras.