Nonrelativistic quantum dynamics on a cone with and without a constraining potential

Abstract

In this paper we investigate the bound state problem of nonrelativistic quantum particles on a conical surface. This kind of surface appears as a topological defect in ordinary semiconductors as well as in graphene sheets. Specifically, we compare and discuss the results stemming from two different approaches. In the first one, it is assumed that the charge carriers are bound to the surface by a constraining potential, while the second one is based on the Klein-Gordon type equation on surfaces, without the constraining potential. The main difference between both theories is the presence/absence of a potential which contains the mean curvature of a given surface. This fact changes the dependence of the bound states on the angular momentum $l$. Moreover, there are bound states that are absent in the Klein-Gordon theory, which instead appear in the Schrödinger one.

Accepted for publication in Journal of Mathematical Physics, 14 pages, 1 figure

References in corpus (5)

• Quantum mechanics on curved 2D systems with electric and magnetic fields
• Cylindrical Two-Dimensional Electron Gas in a Transverse Magnetic Field
• On the quantum dynamics of a point particle in conical space
• Bilayer graphene Origami: curvature-induced p-n junctions
• Aharonov-Bohm-like effect for light propagating in nematics with disclinations

Cited by in corpus (5)

• Remarks on the Aharonov-Casher dynamics in a CPT-odd Lorentz-violating background
• On Aharonov-Casher bound states
• On planar quantum dynamics of a magnetic dipole moment in the presence of electric and magnetic fields
• Influence of spatially varying pseudo-magnetic field on a 2D electron gas in graphene
• Quantum dynamics of a spin-1/2 charged particle in the presence of magnetic field with scalar and vector couplings