Seminar “The Birth of the Schrödinger Equation”
Professor Wolfgang P. Schleich, Chair of Theoretical Physics, Institut für Quantenphysik, Universität Ulm, Germany
Professor Wolfgang P. Schleich is 2018/2019 Sackler Lecturer in the Mortimer and Raymond Sackler Institute of Advanced Studies.
When Erwin Schrödinger was challenged by Peter Debye in a colloquium in Zürich in 1925 to propose a wave equation for matter he understandably faced a tremendous challenge. Therefore, it is not surprising that he first proposed several equations before he settled for the one that we call today the time-dependent Schrödinger equation. Unfortunately, he did not provide much motivation for his choice.
In the present talk we provide a brief history of the birth of the Schrödinger equation and review our work on this topic which centers around three characteristic features of quantum mechanics: (i) it displays a symmetric coupling  between the amplitude and the phase of the quantum wave, (ii) it allows for more freedom in phase  than the one given by the classical action, and (iii) it allows for gauge invariance .
 W.P. Schleich, D.M. Greenberger, D.H. Kobe, and M.O. Scully, The Schrödinger equation revisited, Proc. Nat. Acad. Sci. 110, 5374 (2013)
 W.P. Schleich, D.M. Greenberger, D.H. Kobe, and M.O. Scully, A wave equation interpolating between classical and quantum mechanics, Phys. Scr. 90, 108009 (2015)
 W.P. Schleich, D.M. Greenberger, D.H. Kobe, and M.O. Scully, The birth of the Schrödinger equation, Physics Reports, to be published