Abstract
To quantitatively characterize the behaviors of a spin-12 particle moving on a rotating curved surface and in a time-varying field, we derived the Schrödinger equation of the particle on the surface with the induced Pauli matrices based on the local curvilinear coordinate. To consider the relativistic effects, Minkowski space M is employed. Based on the solution of the Schrödinger equation, we found that the evolution of phase is influenced by the coupling of external fields and the geometry of surfaces as well as the relativistic effect originating from rotation. As examples, the solutions on a rotating cylinder/sphere in a damping magnetic field are calculated. The spin-flip behavior of the particle and the effects of external field and rotation are demonstrated. The results may help stimulate the ideas of modulating and controlling the spin on nano-surfaces.
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