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.

23 pages, a new section on submanifolds of arbitrary dimension and codimension added, references modified and added

References in corpus (2)

• Quantum Mechanics on Manifolds Embedded in Euclidean Space
• Geometric Phase, Curvature, and Extrapotentials in Constrained Quantum Systems

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