Supersymmetry-based Approach to Quantum Particle Dynamics

TL;DR

This paper develops a supersymmetric framework for analyzing the classical and quantum behavior of charged particles on curved surfaces under magnetic fields, revealing shape-invariance properties that enable exact solutions.

Contribution

It introduces a novel N=2 supersymmetric formulation for particle dynamics on curved surfaces, including shape-invariance, facilitating complete quantum solutions.

Findings

Supersymmetric formulation for particle dynamics on curved surfaces.

Identification of shape-invariance in specific geometries.

Exact solutions for quantum problems on spheres and hyperbolic planes.

Abstract

We present the N=2 supersymmetric formulation for the classical and quantum dynamics of a nonrelativistic charged particle on a curved surface in the presence of a perpendicular magnetic field. For a particle moving on a constant-curvature surface in a constant magnetic field, our Hamiltonian possesses the shape-invariance property in addition. On the surface of a sphere and also on the hyperbolic plane, we exploit the supersymmetry and shape-invariance properties to obtain complete solutions to the corresponding quantum mechanical problems.