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

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

Collections

Engineering, Article