The Schrödinger equation is derived assuming the wave function is a probability amplitude and using the de Broglie relations E = ħω and p = ħk for the associated wave.
Dynamical Theories of Brownian Motion; Princeton University Press: 1967
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Derivation of the Schrodinger equation from fundamental principles
The Schrödinger equation is derived assuming the wave function is a probability amplitude and using the de Broglie relations E = ħω and p = ħk for the associated wave.