CONSTRAINED DYNAMICS FOR QUANTUM-MECHANICS - I - RESTRICTING A PARTICLE TO A SURFACE

We analyze constrained quantum systems where the dynamics do not prese rve 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 righ t Hamiltonian on the submanifold when tested on known examples. This m ethod 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 Ameri can Institute of Physics.