Gruppentheorie und Quantenmechanik:The Book and its Position in Weyl’s Work

One of the remarkable facts in the history of Quantum Mechanics is that after Heisenberg’s breakthrough in 1926, most of the important discoveries that were to follow occurred during the next few years. Many of them are connected with Schrödinger’s discovery of wave mechanics. How was this explosion possible? Of course, on the physical side, the ground was prepared by work that had been done since 1900. This is a well known story and need not be repeated here. In an obituary on Wolfgang Pauli, Carl Friedrich von Weizsäcker wrote, “In his article about quantum theory in the first edition of the Blue Handbook (1925) he accomplished the work of art of answering practically every physical question correctly right before the discovery of the quantum mechanics, and therefore with seemingly still inadequate aids.”2 But it is much less well known that on the mathematical side much the same had happened, and only a wrongly placed pride in what they believe to be the autarchy of their own field can prevent physicists from noticing and learning from it. Here two names must be mainly cited (there are others of course): David Hilbert and his great disciple Hermann Weyl.