Quantum particle constrained to a curved surface in the presence of a vector potential

TL;DR

This paper derives the Schrödinger equation for a charged quantum particle on a curved surface with a vector potential, revealing a curvature-dependent coupling term in the limit of surface proximity.

Contribution

It introduces a novel derivation of the Schrödinger equation incorporating curvature effects and vector potential coupling for particles constrained to curved surfaces.

Findings

Coupling term between normal vector potential component and mean curvature.

Derivation method using the form approach.

Insights into quantum behavior on curved geometries.

Abstract

The Schrodinger equation for a charged particle constrained to a curved surface in the presence of a vector potential is derived using the method of forms. In the limit that the particle is brought infinitesimally close to the surface, a term arises that couples the component of the vector potential normal to the surface to the mean curvature of the surface.