Seminar “The Birth of the Schrödinger Equation”

Professor Wolfgang P. Schleich is ​2018/2019 Sackler Lecturer in the Mortimer and Raymond Sackler Institute of Advanced Studies.

Abstract

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 [1] between the amplitude and the phase of the quantum wave, (ii) it allows for more freedom in phase [2] than the one given by the classical action, and (iii) it allows for gauge invariance [3].

[1] W.P. Schleich, D.M. Greenberger, D.H. Kobe, and M.O. Scully, The Schrödinger equation revisited,  Proc. Nat. Acad. Sci. 110, 5374 (2013)

[2] 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)  

[3] W.P. Schleich, D.M. Greenberger, D.H. Kobe, and M.O. Scully, The birth of the Schrödinger equation, Physics Reports, to be published