Realizing holonomic constraints in classical and quantum mechanics

Details Realizing holonomic constraints in classical and quantum mechanics Realizing holonomic constraints in classical and quantum mechanics

1999-09-07

arxiv.org/abs/math-ph/9909007v2

Physics

Mathematical Physics

49 pages

Scientific paper

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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