Quantum particle confined to a thin-layer volume: Non-uniform convergence toward the curved surface

Abstract

We clearly refine the fundamental framework of the thin-layer quantization procedure, and further develop the procedure by taking the proper terms of degree one in $q_3$ ($q_3$ denotes the curvilinear coordinate variable perpendicular to curved surface) back into the surface quantum equation. The well-known geometric potential and kinetic term are modified by the surface thickness. Applying the developed formalism to a toroidal system obtains the modification for the kinetic term and the modified geometric potential including the influence of the surface thickness.

9 pages, 3 figures

References in corpus (6)

• Quantum mechanics on curved 2D systems with electric and magnetic fields
• Visualizing landscapes of the superconducting gap in heterogeneous superconductor thin films: geometric influences on proximity effects
• Aharonov-Bohm effect in the tunnelling of a quantum rotor in a linear Paul trap
• Quantum motion of a point particle in the presence of the Aharonov--Bohm potential in curved space
• Quantum Hall effect in carbon nanotubes and curved graphene strips
• Quantum Theory of Helimagnetic Thin Films

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• Quantum motion of a spinless particle in curved space: A viewpoint of scattering theory
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