Since the amplitudes of classical motions could be squared to find the intensity of the emitted radiation, Heisenberg determined to find a corresponding multiplication rule for the amplitude of virtual oscillators, which would yield the intensity of the spectral lines that had long given physicists trouble. The multiplication rule that Heisenberg devised looked familiar to Born as he critiqued the paper. What Born recognized was that the rule involved the same principle used in multiplying matrices. Before long Born, Jordan, and Heisenberg wrote the groundbreaking paper that expressed quantum physics in matrices. Their equations satisfied the prior principles of quantum physics while accomplishing the long-sought goal of quantifying the discrete energy states of an atom.
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Heisenberg, Schrodinger, famous wave equation, corresponding multiplication rule