- 00-426 Richard Froese and Ira Herbst
- Realizing holonomic constraints in classical and quantum mechanics
Nov 1, 00
(auto. generated ps),
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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.