Dr. Wolfgang Schleich
Mitchell Physics Building
College Station, Texas 77843-4242
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 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.
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