matrixmekanik

Matrix mechanics, sometimes called matrix mechanics (matrixmekanik in Swedish), is one of the original formulations of quantum mechanics. It was developed in 1925 by Werner Heisenberg, Max Born, and Pascual Jordan. The approach replaces classical observables with matrices and describes their dynamics through commutators, rather than using wavefunctions in configuration space.

Core ideas include that physical quantities such as position and momentum are represented by matrices whose elements encode transition amplitudes between quantum states. The noncommutativity of these matrices, exemplified by [x, p] = iħ, leads to the quantization of observables and gives rise to discrete energy spectra in bound systems. The Hamiltonian becomes a matrix, and the stationary states are given by the eigenvalues and eigenvectors of this operator.

Originally developed to explain atomic spectra, matrix mechanics established the language of operators and matrices that underpins quantum theory. In 1926, Schrödinger introduced wave mechanics, and later it was shown that matrix mechanics and wave mechanics are mathematically equivalent representations of the same theory, related by unitary transformations (transformation theory). In the Heisenberg picture, operators carry time dependence while state vectors are fixed; in the Schrödinger picture, states evolve in time according to the Schrödinger equation.

Matrix mechanics laid the groundwork for modern quantum mechanics and, through its operator formalism, foreshadowed quantum field theory. While often presented alongside wave mechanics, its primary contribution is the realization that observable quantities can be treated as matrices with algebraic relations, yielding the correct predictions for spectra, transition rates, and selection rules.