SchrSdinger Equation of a Particle on a Rotating Curved Surface

充宏 池上

伸 高木

Shin Takagi

M. S. Shikakhwa, Noureddine Chair

Long Du, Yong-Long Wang, Guo-Hua Liang +2 more

We derive the Schrödinger equation of a particle constrained to move on a rotating curved surface S. Using the thin-layer quantization scheme to confine the particle on S, and with a proper choice of gauge transformation for the wave function, we obtain the well-known geometric potential V g and an additive Coriolis-induced geometric potential in the co-rotational curvilinear coordinates. This novel effective potential, which is included in the surface Schrödinger equation and is coupled with the mean curvature of S, contains an imaginary part in the general case which gives rise to a non-Hermitian surface Hamiltonian. We find that the non-Hermitian term vanishes when S is a minimal surface or a revolution surface which is axially symmetric around the rolling axis.

Run Cheng, Li Wang, Hao Zhao +2 more

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.