99-326 Richard Froese and Ira Herbst

Realizing holonomic constraints in classical and quantum mechanics (342K, ps, pdf) Sep 7, 99

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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.

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