Supersymmetry-Based Approach to Quantum Particle Dynamics on a Curved Surface with Non-zero Magnetic Field

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 posses...

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Bibliographic Details
Published in:Annals of physics 2002-03, Vol.296 (2), p.390-405
Main Authors: Kim, Seok, Lee, Choonkyu
Format: Article
Language:English
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Summary: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.
ISSN:0003-4916
1096-035X
DOI:10.1006/aphy.2002.6224