Schrödinger equations in constrained space with several initial constraints

A general system constrained with {\it several} initial constraint conditions is quantized based on the Dirac formalism and the Schrödinger equation for this system is obtained. These constraint conditions are now allowed to depend not only on the coordinates but also on the velocities. It is shown that the hermiticity for the observables of the system restricts the geometrical structure of our world. A general system constrained with {\it several} initial constraint conditions is quantized based on the Dirac formalism and the Schrödinger equation for this system is obtained. These constraint conditions are now allowed to depend not only on the coordinates but also on the velocities. It is shown that the hermiticity for the observables of the system restricts the geometrical structure of our world