Each quantity was represented by a collection of Fourier coefficients with two indices, corresponding to the initial and final states. The quantities in Heisenberg's formulation were the classical position and momentum, but now they were no longer sharply defined. Classically, the Fourier coefficients give the intensity of the emitted radiation, so in quantum mechanics the magnitude of the matrix elements of the position operator were the intensity of radiation in the bright-line spectrum. He replaced the classical Fourier series with a matrix of coefficients, a fuzzed-out quantum analog of the Fourier series. Heisenberg, after a collaboration with Kramers, began to understand that the transition probabilities were not quite classical quantities, because the only frequencies that appear in the Fourier series should be the ones that are observed in quantum jumps, not the fictional ones that come from Fourier-analyzing sharp classical orbits. But his answer, like all other calculations in the old quantum theory, was only correct for large orbits. Hendrik Kramers had earlier calculated the relative intensities of spectral lines in the Sommerfeld model by interpreting the Fourier coefficients of the orbits as intensities. In the paper, Heisenberg formulated quantum theory without sharp electron orbits. Heisenberg then departed for a while, leaving Born to analyse the paper. On July 9 Heisenberg gave the same paper of his calculations to Max Born, saying that "he had written a crazy paper and did not dare to send it in for publication, and that Born should read it and advise him" prior to publication. ![]() ![]() The three fundamental papers Īfter Heisenberg returned to Göttingen, he showed Wolfgang Pauli his calculations, commenting at one point:Įverything is still vague and unclear to me, but it seems as if the electrons will no more move on orbits. So I left the house and awaited the sunrise on the top of a rock. I was so excited that I could not think of sleep. It was about three o' clock at night when the final result of the calculation lay before me. While there, in between climbing and memorizing poems from Goethe's West-östlicher Diwan, he continued to ponder the spectral issue and eventually realised that adopting non-commuting observables might solve the problem. On June 7, after weeks of failing to alleviate his hay fever with aspirin and cocaine, Heisenberg left for the pollen-free North Sea island of Helgoland. By May 1925 he began trying to describe atomic systems by observables only. In 1925 Werner Heisenberg was working in Göttingen on the problem of calculating the spectral lines of hydrogen. In 1925, Werner Heisenberg, Max Born, and Pascual Jordan formulated the matrix mechanics representation of quantum mechanics. Relying on these methods, Wolfgang Pauli derived the hydrogen atom spectrum in 1926, before the development of wave mechanics. ![]() In some contrast to the wave formulation, it produces spectra of (mostly energy) operators by purely algebraic, ladder operator methods. ![]() It is equivalent to the Schrödinger wave formulation of quantum mechanics, as manifest in Dirac's bra–ket notation. It did so by interpreting the physical properties of particles as matrices that evolve in time. Its account of quantum jumps supplanted the Bohr model's electron orbits. It was the first conceptually autonomous and logically consistent formulation of quantum mechanics. Matrix mechanics is a formulation of quantum mechanics created by Werner Heisenberg, Max Born, and Pascual Jordan in 1925.
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