Abstract
Recently, a theory of fractal space-time has been proposed to unify the huge number of axioms of quantum mechanics, and one of the keys of this approach is the introduction of a complex-valued velocity which is a combination of the forward derivative (derivative on the right) with the backward derivative (derivative on the left) of the state co-ordinate vector. It is shown that if instead, one uses the classical velocity (forward derivative) but with complex-valued increments for the admissible variations of the state, it is possible to derive Schrödinger equation in exactly the same manner. The prospect of this alternative is to provide a generalization by using complex-valued Brownian motion.
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