Heisenberg's achievement came at a time when all of his colleagues were working on different tangents, and with no systematic approach to the answers they all desired. Nevertheless, their topics of research often complemented each other in unexpected ways. While Born and his new assistant Pascual Jordan were working on the quantum theory of aperiodic systems, Heisenberg returned to the problem of virtual oscillators in the atom. The amplitude of the oscillations could be broken down to a Fourier series, but what Heisenberg recognized was that this function had continued to use classical relationships. Assuming that the basic Fourier function held true on the quantum level, he then set about reinterpreting the frequencies and amplitude with quantum principles in mind, as he had in formulating the Zeeman principle.
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