  The central limit theorem has been found to apply to random vectors in
complex Hilbert space. This amounts to sufficient reason to study the complex
valued Gaussian, looking for relevance to quantum mechanics. Here we show that
the Gaussian, with all terms fully complex, acting as a propagator, leads to
Schrodinger nonrelativistic equation including scalar and vector potentials,
assuming only that the norm is conserved. No prior physical laws need to be
postulated. It thereby presents as a process of irregular motion analogous to
the real random walk but executed under the rules of the complex number system.
Inferences are 1. There is a standard view that Schrodinger equation is
deterministic, while wavefunction collapse is probabilistic by Born's rule.
This is opposed by the now demonstrated linkage to the central limit theorem,
indicating a stochastic picture for the foundation of Schrodinger equation
itself. 2. This picture is also consistent with the dynamic origin of
probabilities suggested for the Born rule in the de Broglie Bohm pilot wave
theory. Reasons for the primary role of C are open to discussion. The present
derivation is compared with recent reconstructions of the quantum formalism,
which have the aim of rationalizing its obscurities.
