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arXiv · 1310.6651

Quantum dynamics of a particle constrained to lie on a surface

Gustavo de Oliveira
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Abstract

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 extend previous results by allowing magnetic potentials and more general constraining potentials.

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Gustavo de Oliveira. 2014-09-04. Quantum dynamics of a particle constrained to lie on a surface. https://doi.org/10.1063/1.4895761

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