Schr?dinger Equation of a Particle on a Rotating Curved Surface

doi:10.1088/0256-307X/33/3/030301

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 Wang^1,2, Guo-Hua Liang¹, Guang-Zhen Kang¹, Hong-Shi Zong^2,3,4

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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