Axiomatic Basis of Quantum Mechanics
Ahmad Amer
This chapter introduces an elementary form of the fundamental axioms of quantum mechanics, focusing on the structure and interpretation of state functions within a vector space framework. The properties of linear operators acting on state functions are explored, along with the physical meaning of the state function itself. From this interpretation, boundary conditions and normalization requirements are derived. The chapter presents key results such as the normalization theorem, the time derivative of a physical observable, and Ehrenfest's theorem. It also defines probability density and probability current density, deriving the continuity equation for probability. The uncertainty principle is formally established, and energy conservation is addressed. The eigenvalues and eigenstates of the momentum operator are determined, and normalization using the Dirac delta function is introduced. The free particle wavefunction is derived, concluding with a discussion on the classical limit of quantum mechanics. Metadata/Keywords: quantum axioms, state function, linear operators, probability density, probability current, Ehrenfest's theorem, uncertainty principle, Dirac delta function, momentum eigenstates, classical limit
CRC Press eBooks•Nov 5, 2025•0 citations