Semiclassical analysis of constrained quantum systems
Abstract
We study the dynamics of a quantum particle in R(n+m) constrained by a strong potential force to stay within a distance of order hbar (in suitable units) from a smooth n-dimensional submanifold M. We prove that in the semiclassical limit the evolution of the wave function is approximated in norm, up to terms of order hbar(1/2), by the evolution of a semiclassical wave packet centred on the trajectory of the corresponding classical constrained system.
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