Quantum-Mechanical Particle Confined to Surfaces of Revolution - Truncated Cone and Elliptic Torus Case Studies

Jens Gravesen, Morten Willatzen, L.C. Lew Yan Voon

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    Abstract

    The theory of a quantum-mechanical particle confined to a surface of revolution is described using differential geometry methods including the derivation of a general set of three ordinary differential equations in curved coordinates. The problem is shown to be completely separable with the present hard-wall boundary conditions. Two case studies of recent experimental interest. the nanocone and torus-shaped nanoring structures. are analyzed in terms of eigenstates, energies. and symmetry characteristics based on the theory presented.
    Original languageEnglish
    JournalPhysica Scripta
    Volume72
    Issue number2-3
    Pages (from-to)105-111
    ISSN0031-8949
    DOIs
    Publication statusPublished - 2005

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