The solution of the difficulty is that the two mental pictures which experiment lead us to form - the one of the particles, the other of the waves - are both incomplete and have only the validity of analogies which are accurate only in limiting cases.

His thinking on Dirac's theory and further development of the theory were set forth in two papers. Per Heisenberg. In Heisenberg's tenure at Leipzig the quality of doctoral students post-graduate and research associates who studied and worked with Heisenberg there is attested to by the acclaim later earned by these people; at various times they included: Erich Bagge Felix Bloch Ugo Fano Siegfried Flügge William Vermillion Houston Friedrich Hund Robert S.

He also made important contributions to the theories of the hydrodynamics of turbulent flows the atomic nucleus ferromagnetism cosmic rays and subatomic particles and he was instrumental in planning the first West German nuclear reactor at Karlsruhe together with a research reactor in Munich in 1957. Heisenberg along with Max Born and Pascual Jordan set forth the matrix formulation of quantum mechanics in 1925. Considerable controversy surrounds his work on atomic research during World War II.