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.