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,[1][2] was a breakthrough article in quantum mechanics written by Werner Heisenberg, which appeared in Zeitschrift für Physik in September 1925.In the article, Heisenberg tried to explain the energy levels of a one-dimensional anharmonic oscillator, avoiding the concrete but unobservable representations of electron orbits by using observable parameters such as transition probabilities for quantum jumps, which necessitated using two indexes corresponding to the initial and final states.[7] Heisenberg was 23 years old when he worked on the article while recovering from hay fever on the island of Heligoland, corresponding with Wolfgang Pauli on the subject.[4] A follow-on article by all three authors extending the theory to multiple dimensions was submitted for publication before the end of the year.But Heisenberg saw that "the simplest and most natural assumption would be"[9]: 275f to follow the lead provided by recent work in computing light dispersion done by Hans Kramers.Paul Dirac, who had received a proof copy in August 1925, realized that the commutative law had not been fully developed, and he produced an algebraic formulation to express the same results in more logical form.Heisenberg's teacher saw almost immediately that his work should be expressed in a matrix format because mathematicians already were familiar with how to do computations involving matrices in an efficient way.Werner Heisenberg used the idea that since classical physics is correct when it applies to phenomena in the world of things larger than atoms and molecules, it must stand as a special case of a more inclusive quantum theoretical model.So he hoped that he could modify quantum physics in such a way that when the parameters were on the scale of everyday objects it would look just like classical physics, but when the parameters were pulled down to the atomic scale the discontinuities seen in things like the widely spaced frequencies of the visible hydrogen bright line spectrum would come back into sight.The one thing that people at that time most wanted to understand about hydrogen radiation was how to predict or account for the intensities of the lines in its spectrum.Heisenberg's great advance was the "scheme which was capable in principle of determining uniquely the relevant physical qualities (transition frequencies and amplitudes)"[12]: 2 of hydrogen radiation.Heisenberg ... took leave of absence ... and handed over his paper to me for publication ... Heisenberg's rule of multiplication left me no peace, and after a week of intensive thought and trial, I suddenly remembered an algebraic theory....Such quadratic arrays are quite familiar to mathematicians and are called matrices, in association with a definite rule of multiplication.