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By considering a random walk model compounded in Einstein's evolution equation, we show that both the classical Schrodinger and Klein-Gordon equations can be viewed a s consequence of introducing a memory function.
The purpose of this is to derive a wave equaiton that, on a phenomenological basis at least, describes the transitional characteristics of wave functions for spin-less particles that may exist in the intermediate of "semi relativistic regime.
Blackledge, J., Babajanov, B. (2013) : The Fractional Schrodinger-Klein-Gordon Equation and Intermediate Relativism. Mathematic Aeterna, Vol.3, 2013, no. 8, p.601 - 615. doi:10.21427/D7F03C