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arXiv · 1502.02110

Quantum particle confined to a thin-layer volume: Non-uniform convergence toward the curved surface

Yong-Long Wang·Hong-Shi Zong
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Abstract

We clearly refine the fundamental framework of the thin-layer quantization procedure, and further develop the procedure by taking the proper terms of degree one in $q_3$ ($q_3$ denotes the curvilinear coordinate variable perpendicular to curved surface) back into the surface quantum equation. The well-known geometric potential and kinetic term are modified by the surface thickness. Applying the developed formalism to a toroidal system obtains the modification for the kinetic term and the modified geometric potential including the influence of the surface thickness.

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Yong-Long Wang, Hong-Shi Zong. 2015-02-07. Quantum particle confined to a thin-layer volume: Non-uniform convergence toward the curved surface. https://doi.org/10.1016/j.aop.2015.10.019

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