THE THIRD WAY TO QUANTUM MECHANICS IS THE FORGOTTEN FIRST by Salvatore ANTOCI and Dierck-E. LIEBSCHER

Quantum mechanics can be formulated in three ways, as Heisenberg, Schrödinger and Feynman did respectively. For the last way, an unknown (i.e. forgotten) forerunner exists, that we have found in a paper by Gregor Wentzel, published before the famous works by Heisenberg and Schrödinger, and contemporary with the fundamental works of L. de Broglie. In that paper, one can find the basic formulae and their interpretation as they were adopted by Feynman twenty years later. We believe that Wentzel’s work was forgotten for several reasons: (I) Schrödinger’s equation was much simpler to deal with (Wentzel himself contributed to its development in the same way as L.Brillouin and H.Kramers did). (II) The first application was rejected by Heisenberg and Kramers. (III) The approximation used by Wentzel was too näıve and failed. Nevertheless, the foundation laid by Wentzel was sound, as it has been shown by Feynman’s work. Therefore, Wentzel has to be considered as one of the founders of quantum mechanics. Our exposition aims at explaining some details. It is accompanied by two appendices. They respectively provide a summary of the quoted paper by Wentzel and of the theory of canonical transformations, needed to understand the link between Wentzel’s and Feynman’s formulations. Dipartimento di Fisica “Alessandro Volta” dell’ Università degli Studi di Pavia, Via Bassi 6, I-27100 Pavia, phone +39-382-507-486, fax +39-382-507-563 Astrophysikalisches Institut Potsdam, An der Sternwarte 16, D-14482 Potsdam, email: [email protected], phone +49-331-7499-231, fax +49-331-7499-309