A Generalized Nonlinear Extension of Quantum Mechanics

We construct the most general form of our previously proposed nonlinear extension of quantum mechanics that possesses three basic properties. Unlike the simpler model, the new version is not completely integrable, but it has an underlying Hamiltonian structure. We analyze a particular solution in detail, and we use a natural extension of the Born rule to compute particle trajectories. We find that closed particle orbits are possible.