A new paper looks at the origins of the Schrodinger's equation and describes how Schrödinger derived it. The classical solution is a nonlinear wave equation but the quantum mechanic solution is linear wave equation. In quantum mechanics, the amplitude and phase depend on each other making the Schrödinger equation linear. This linearity allows for the superposition of states. The full paper by Wolfgang P. Schleich, et al. titled Schrödinger equation revisited sounds fascinating. I wish I had access to it.