Physics Letters, Section A: General, Atomic and Solid State Physics, vol.380, no.36, pp.2876-2880, 2016 (SCI-Expanded)
The Schrödinger 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 Schrödinger Hamiltonians on the surfaces of a cylinder, a sphere and a torus are derived.