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A spin-less particle on a rotating curved surface in Minkowski space
Authors:Run Cheng  Li Wang  Hao Zhao  Cui-Bai Luo  Yong-Long Wang  Jun Wang
Institution:1.National Lab of Solid State Microstructure, Collaborative Innovation Center of Advanced Microstructures, and School of Physics, Nanjing University, Nanjing 210093, China;2.School of Physics and Electronic Engineering, Linyi University, Linyi 276005, China;3.Department of Physics, Anhui Normal University, Wuhu 241002, China
Abstract:In Minkowski space ${ \mathcal M }$, we derive the effective Schrödinger equation describing a spin-less particle confined to a rotating curved surface ${ \mathcal S }$. Using the thin-layer quantization formalism to constrain the particle on ${ \mathcal S }$, we obtain the relativity-corrected geometric potential ${V}_{g}^{{\prime} }$, and a novel effective potential ${\tilde{V}}_{g}$ related to both the Gaussian curvature and the geodesic curvature of the rotating surface. The Coriolis effect and the centrifugal potential also appear in the equation. Subsequently, we apply the surface Schrödinger equation to a rotating cylinder, sphere and torus surfaces, in which we find that the interplays between the rotation and surface geometry can contribute to the energy spectrum based on the potentials they offer.
Keywords:rotating curved surface  Minkowski space  surface Schrödinger equation  curvature  
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