How to Derive the Schrodinger Equation
  We illustrate a simple derivation of the Schrodinger equation, which requires only knowledge of the electromagnetic wave equation and the basics of Einstein's special theory of relativity. We do this by extending the wave equation for classical fields to photons, generalize to non-zero rest mass particles, and simplify using approximations consistent with non-relativistic particles. 
David W. Ward, Sabine M. Volkmer