491 research outputs found
Derivation of the Schr\"odinger equation from classical stochastic dynamics
From classical stochastic equations of motion we derive the quantum
Schr\"odinger equation. The derivation is carried out by assuming that the real
and imaginary parts of the wave function are proportional to the
coordinates and momenta associated to the degrees of freedom of an underlying
classical system. The wave function is assumed to be a complex time
dependent random variable that obeys a stochastic equation of motion that
preserves the norm of . The quantum Liouville equation is obtained by
considering that the stochastic part of the equation of motion changes the
phase of but not its absolute value. The Schr\"odinger equation follows
from the Liouville equation. The wave function obeying the Schr\"odinger
equation is related to the stochastic wave function by
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