As I understand (from reading p. 2-06 of Marle's 1975 text on geometric quantization available on the french wiki page on "quantification géométrique") , there are physical situations where we do not know how to write the Schrodinger equation. Namely, we do not know what operator to take as the hamiltonian H in the equation dψ/dt = Hψ. Is this correct? What is the simplest physical system where this situation occurs? Thanks.