کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
1858883 | 1037172 | 2016 | 5 صفحه PDF | دانلود رایگان |
• New physical approach to confine particles to curved surfaces.
• Confinement of a particle in a magnetic field to a surface is gauge-independent.
• Spin one-half particle with SO coupling confined to a surface.
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.
Journal: Physics Letters A - Volume 380, Issue 36, 19 August 2016, Pages 2876–2880