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Hamiltonian for a particle in a magnetic field on a curved surface in orthogonal curvilinear coordinates
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Date
2016-08-19
Author
Shikakhwa, M. S.
Chair, N.
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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.
Subject Keywords
Quantum mechanics on curved surfaces
,
Pauli Hamiltonian on a curved surface
,
Spin-orbit coupling
,
Geometric momentum
URI
https://hdl.handle.net/11511/64441
Journal
PHYSICS LETTERS A
DOI
https://doi.org/10.1016/j.physleta.2016.06.024
Collections
Engineering, Article
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M. S. Shikakhwa and N. Chair, “Hamiltonian for a particle in a magnetic field on a curved surface in orthogonal curvilinear coordinates,”
PHYSICS LETTERS A
, pp. 2876–2880, 2016, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/64441.