Employing the Staticization Operator in Conservative Dynamical Systems and the Schrödinger Equation

Conservative dynamical systems propagate as stationary points of the action functional. Hence, dynamical-systems questions may be addressed by control-theoretic methods. Using this representation, it has previously been demonstrated that one may obtain fundamental solutions for two-point boundary value problems for some classes of conservative systems via solution of an associated dynamic program. It is also known that the gravitational and Coulomb potentials may be represented as stationary points of cubicly-parameterized quadratic functionals. Hence, stationary points of the action functional may be represented via iterated staticization of polynomial functionals. This leads to representations through operations on sets of solutions of differential Riccati equations (DREs). A key step in this process is the reordering of staticization operations.