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 focused exclusively on observable parameters, parameters that could be measured in scientific experiments, such as transition probabilities or frequencies associated with quantum jumps in spectral lines. This contrasted with earlier quantum theories that focused on unobservable parameters, like the position or velocity of electrons in electron orbits. In contrast to other quantum theories, Heisenberg assumed that issues stemmed from the kinematics (how position and velocity were defined) in the old quantum theory, not classical equations of motion.

Mathematically, Heisenberg used two indices for his reinterpretation of position, corresponding to initial and final states of quantum jumps. In addition, Heisenberg introduced non-commutative operators in a new multiplication rule, i.e. generally

A

B

≠

B

A

{\displaystyle AB\neq BA}

for quantum quantities

A

{\displaystyle A}

and

B

{\displaystyle B}

. This insight would later become the basis for Heisenberg's uncertainty principle. Heisenberg used his framework to successfully explain the energy levels of a one-dimensional anharmonic oscillator.

The Umdeutung paper was followed by another paper by Max Born and Pascual Jordan in 1925 that built on the Umdeutung paper's conceptual framework, and by the 'three-man paper' (German: Dreimännerarbeit) by Born, Heisenberg and Jordan in 1926.