Quantum dynamics of a particle constrained to lie on a surface
arXiv:1310.6651 · doi:10.1063/1.4895761
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.
arXiv commentFinal version to appear in J. Math. Phys
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Cited by in corpus (6)
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- Derivation of the 2d Gross-Pitaevskii equation for strongly confined 3d bosons
- On an extension of the Iwatsuka model
- Sphere on a plane: Two-dimensional scattering from a finite curved region