Quantum dynamics of a particle constrained to lie on a surface

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.

Final version to appear in J. Math. Phys

References in corpus (1)

• Quantum mechanics on curved 2D systems with electric and magnetic fields

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