Dirac equation on a catenoid bridge: a supersymmetric approach

TL;DR

This paper investigates the Dirac equation on a catenoid surface, deriving analytical solutions using supersymmetric quantum mechanics for different Fermi velocity scenarios, advancing understanding of relativistic electrons on curved geometries.

Contribution

It introduces a supersymmetric approach to solving the Dirac equation on a catenoid, including cases with constant and position-dependent Fermi velocities, which is a novel application.

Findings

Analytical solutions for Dirac electrons on a catenoid surface.

Decoupling of spinor components into Klein-Gordon-like equations.

Application of supersymmetric quantum mechanics to curved surface problems.

Abstract

In this paper, we study the Dirac equation for an electron constrained to move on a catenoid surface. We decoupled the two components of the spinor and obtained two Klein-Gordon-like equations. Analytical solutions were obtained using supersymmetric quantum mechanics for two cases, namely, the constant Fermi velocity and the position-dependent Fermi velocity cases.