Chin. Phys. Lett.  2016, Vol. 33 Issue (03): 030301    DOI: 10.1088/0256-307X/33/3/030301
GENERAL |
Schr?dinger Equation of a Particle on a Rotating Curved Surface
Long Du1, Yong-Long Wang1,2, Guo-Hua Liang1, Guang-Zhen Kang1, Hong-Shi Zong2,3,4
1Department of Physics, Nanjing University, Nanjing 210093
2Department of Physics, School of Science, Linyi University, Linyi 276005
3Joint Center for Particle, Nuclear Physics and Cosmology, Nanjing 210093
4State Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190
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Long Du, Yong-Long Wang, Guo-Hua Liang et al  2016 Chin. Phys. Lett. 33 030301
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Abstract We derive the Schr?dinger 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 $V_{\rm g}$ and an additive Coriolis-induced geometric potential in the co-rotational curvilinear coordinates. This novel effective potential, which is included in the surface Schr?dinger 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.
Received: 01 October 2015      Published: 31 March 2016
PACS:  03.65.-w (Quantum mechanics)  
  02.40.-k (Geometry, differential geometry, and topology)  
  68.65.-k (Low-dimensional, mesoscopic, nanoscale and other related systems: structure and nonelectronic properties)  
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https://cpl.iphy.ac.cn/10.1088/0256-307X/33/3/030301       OR      https://cpl.iphy.ac.cn/Y2016/V33/I03/030301
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Long Du
Yong-Long Wang
Guo-Hua Liang
Guang-Zhen Kang
Hong-Shi Zong
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