Schrödinger problems for surfaces of revolution—the finite cylinder as a test example

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  • Jens Gravesen
    Mads Clausen Institute for Product Innovation , University of Southern Denmark, Grundtvigs Allé 150, DK-6400 Sønderborg, Denmark
  • Morten Willatzen
    Mads Clausen Institute for Product Innovation , University of Southern Denmark, Grundtvigs Allé 150, DK-6400 Sønderborg, Denmark
  • L. C. Lew Yan Voon
    Department of Physics , Worcester Polytechnic Institute, Worcester, Massachusetts 01609

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<jats:p>A set of ordinary differential equations is derived employing the method of differentiable forms so as to describe the quantum mechanics of a particle constrained to move on a general two-dimensional surface of revolution. Eigenvalues and eigenstates are calculated quasianalytically in the case of a finite cylinder (finite along the axis) and compared with the eigenvalues and eigenstates of a full three-dimensional Schrödinger problem corresponding to a hollow cylinder in the limit where the inner and outer radii approach each other. Good agreement between the two models is obtained for a relative difference less than 20% in inner and outer radii.</jats:p>

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