Richard Froese and Ira Herbst
Realizing holonomic constraints in classical and quantum mechanics
(342K, ps, pdf)

ABSTRACT.  We consider the problem of constraining a particle to a submanifold 
$\Sigma$ of configuration space using a sequence of increasing 
potentials. We compare the classical and quantum versions of this 
procedure. This leads to new results in both cases: an unbounded 
energy theorem in the classical case, and a quantum averaging 
theorem. Our two step approach, consisting of an expansion in a 
dilation parameter, followed by averaging in normal directions, 
emphasizes the role of the normal bundle of $\Sigma$, and shows 
when the limiting phase space will be larger (or different) than 
expected.