The linearity of quantum mechanics and the birth of the Schroedinger equation

Wolfgang P. Schleich

Universität Ulm, Institut für Quantenphysik, Ulm, Germany

The time-dependent Schroedinger equation is a cornerstone of quantum physics and governs all phenomena of the microscopic world. However, despite its importance its origin is still not fully understood. We obtain the Schroedinger equation from the Hamilton-Jacobi equation of classical mechanics together with the law of conservation of matter. It is the quantum current in this continuity equation which ensures the linearity of quantum mechanics.

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