Umdeutung paper

In the history of physics, "On the quantum-theoretical reinterpretation of kinematical and mechanical relationships" (German: Über quantentheoretische Umdeutung kinematischer und mechanischer Beziehungen), also known as the Umdeutung (reinterpretation) paper, was a breakthrough article in quantum mechanics written by Werner Heisenberg, which was published in Zeitschrift für Physik in July 1925.

In his article, Heisenberg described a new framework for quantum theory that was based on observable parameters (parameters that could be measured in scientific experiments), such as transition probabilities or frequencies associated with quantum jumps in spectral lines, rather than unobservable parameters, like the position or velocity of electrons in electron orbits. Thus, Heisenberg used two indices for his reinterpretation of position, corresponding to initial and final states of quantum jumps. Heisenberg used his framework to successfully explain the energy levels of a one-dimensional anharmonic oscillator.

Mathematically, Heisenberg used non-commutative operators in his new multiplication rule, i.e. generally ${\displaystyle AB\neq BA}$ for quantum quantities ${\displaystyle A}$ and ${\displaystyle B}$. This insight would later become the basis for Heisenberg's uncertainty principle.

This article was followed by the paper by Max Born and Pascual Jordan of the same year, building on the conceptual ideas of the Umdeutung paper, and by the 'three-man paper' (German: Dreimännerarbeit) by Born, Heisenberg and Jordan in 1926. These following articles along with the Umdeutung paper laid the groundwork for matrix mechanics that would come to substitute old quantum theory, becoming the first mature mathematical formulation of quantum mechanics. Heisenberg received the Nobel Prize in Physics in 1932 for his work on developing quantum mechanics.