Schrödinger equation for quantum fractal space-time of order \(n\) via the complex-valued fractional Brownian motion. (Q2783572)

After providing some background on the Schrödinger equation, quantum fractal space-time and ``complex Brownian motion of order \(n\)'', the author proposes a set of axioms for the quantum mechanical description of a physical system and sets out to derive the Schrödinger equation from these. In particular, he assumes that each component of a system in \({\mathbb R}^3\) is described by a ``complex-valued Brownian motion of order \(n\)''. This ``complex-valued Brownian motion'' seems to have some similarity with two-dimensional fractional Brownian motion with Hurst index \(1/n\), but the reviewer has doubts about the positivity of the probability density calculated in this paper. Jumarie also discusses the relevance of the Schrödinger equation of order \(n\), relativistic quantum mechanics of order \(n\), and the free particle Klein-Gordon equation of order \(n\).