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Title: Quantum dynamics of a particle constrained to lie on a surface

We consider the quantum dynamics of a charged particle in Euclidean space subjected to electric and magnetic fields under the presence of a potential that forces the particle to stay close to a compact surface. We prove that, as the strength of this constraining potential tends to infinity, the motion of this particle converges to a motion generated by a Hamiltonian over the surface superimposed by an oscillatory motion in the normal directions. Our result extends previous results by allowing magnetic potentials and more general constraining potentials.
Authors:
 [1]
  1. Institute for Applied Mathematics, University of Bonn, Endenicher Allee 60, 53115 Bonn (Germany)
Publication Date:
OSTI Identifier:
22306034
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Mathematical Physics; Journal Volume: 55; Journal Issue: 9; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; CHARGED PARTICLES; EUCLIDEAN SPACE; HAMILTONIANS; MAGNETIC FIELDS; PARTICLES; POTENTIALS