{
  "id": "1610.09663",
  "version": "v1",
  "published": "2016-10-30T15:33:14.000Z",
  "updated": "2016-10-30T15:33:14.000Z",
  "title": "Hermitian and Gauge-Covariant Hamiltonians for a particle in a magnetic field on Cylindrical and Spherical Surfaces",
  "authors": [
    "M. S. Shikakhwa",
    "N. Chair"
  ],
  "comment": "8 pages, no figures",
  "categories": [
    "quant-ph",
    "cond-mat.mes-hall"
  ],
  "abstract": "We construct the Hermitian Schr\\\"{o}dinger Hamiltonian of spin-less as well as the gauge-covariant Pauli Hamiltonian of spin one-half particles in a magnetic field that are confined to cylindrical and spherical surfaces. The approach does not require the use of involved differential-geometrical methods and is intuitive and physical, relying on the general requirements of Hermicity and gauge-covariance. The surfaces are embedded in the full three-dimensional space and confinement to the surfaces is achieved by strong radial potentials. We identify the Hermitian and gauge-covariant (in the presence of a magnetic field) physical radial momentum in each case and set it to zero upon confinement to the surfaces . The resulting surface Hamiltonians are seen to be automatically Hermitian and gauge-covariant. The well-known geometrical kinetic energy also emerges naturally.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-10-30T15:33:14.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "magnetic field",
      "spherical surfaces",
      "gauge-covariant hamiltonians",
      "gauge-covariant pauli hamiltonian",
      "spin one-half particles"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}