This looks like an interesting paper on the mathematical structure that makes the Schrödinger equation linear, and how it’s related to the classical (nonlinear) Hamilton-Jacobi equation.

I’d be interested to compare their approach to the the formulation of Bohm’s (hidden-variable quantum) theory that casts the equations of motion as a Hamilton-Jacobi equation with an extra (nonlocal) quantum potential. Food for thought.

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