  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 Euclidean n-space to a curved submanifold, and we propose a method
of constraining and dynamics adjustment which produces the right Hamiltonian on
the submanifold when tested on known examples. This method we hope will become
the germ of a full Dirac algorithm for quantum constraints. We take a first
step in generalising it to the situation where the constraint is a general
selfadjoint operator with some additional structures.
