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
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- Morten Willatzen
- Mads Clausen Institute for Product Innovation , University of Southern Denmark, Grundtvigs Allé 150, DK-6400 Sønderborg, Denmark
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- L. C. Lew Yan Voon
- Department of Physics , Worcester Polytechnic Institute, Worcester, Massachusetts 01609
抄録
<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>
収録刊行物
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- Journal of Mathematical Physics
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Journal of Mathematical Physics 46 (1), 2005-01-01
AIP Publishing