Constrained dynamics for quantum mechanics. I. Restricting a particle to a surface

We analyze constrained quantum systems where the dynamics do not preserve the constraints. This is done, in particular, for the restriction of a quantum particle in R-n to a curved submanifold, and we propose a method of constraining and dynamics adjustment that produces the right Hamiltonian on the submanifold when tested on known examples. This method will be the germ of a "Dirac algorithm for quantum constraints." We generalize it to the situation where the constraint is a general self-adjoint operator with some additional structures. (C) 1998 American Institute of Physics.