Hamiltonian for a particle in a magnetic field on a curved surface in orthogonal curvilinear coordinates


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Shikakhwa M. S. , Chair N.

PHYSICS LETTERS A, vol.380, no.36, pp.2876-2880, 2016 (Peer-Reviewed Journal) identifier identifier

  • Publication Type: Article / Article
  • Volume: 380 Issue: 36
  • Publication Date: 2016
  • Doi Number: 10.1016/j.physleta.2016.06.024
  • Journal Name: PHYSICS LETTERS A
  • Journal Indexes: Science Citation Index Expanded, Scopus
  • Page Numbers: pp.2876-2880
  • Keywords: Quantum mechanics on curved surfaces, Geometric momentum, Spin-orbit coupling, Pauli Hamiltonian on a curved surface, QUANTUM-MECHANICS, ORBIT

Abstract

The Schrodinger Hamiltonian of a spin-less particle as well as the Pauli Hamiltonian with spin-orbit coupling included of a spin one-half particle in electromagnetic fields that are confined to a curved surface embedded in a three-dimensional space spanned by a general Orthogonal Curvilinear Coordinate are constructed. A new approach, based on the physical argument that upon squeezing the particle to the surface by a potential, then it is the physical gauge-covariant kinematical momentum operator (velocity operator) transverse to the surface that should be dropped from the Hamiltonian(s). In both cases, the resulting Hermitian gauge-invariant Hamiltonian on the surface is free from any reference to the component of the vector potential transverse to the surface, and the approach is completely gauge-independent. In particular, for the Pauli Hamiltonian these results are obtained exactly without any further assumptions or approximations. Explicit covariant plug-and-play formulae for the Schrodinger Hamiltonians on the surfaces of a cylinder, a sphere and a torus are derived. (C) 2016 Elsevier B.V. All rights reserved.