Semiclassical analysis of constrained quantum systems

Details Semiclassical analysis of constrained quantum systems Semiclassical analysis of constrained quantum systems

2003-12-11

arxiv.org/abs/math-ph/0312034v2

Journal of Physics A: Mathematical and General, volume 37, 5605-5624 (2004)

Physics

Mathematical Physics

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

Scientific paper

10.1088/0305-4470/37/21/007

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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