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

Обложка книги Schrödinger problems for surfaces of revolution-the finite cylinder as a test example

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

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A set of ordinary differential equations is derived employing the method of differentiableforms so as to describe the quantum mechanics of a particle constrained tomove on a general two-dimensional surface of revolution. Eigenvalues and eigenstatesare calculated quasianalytically in the case of a finite cylinder (finite alongthe axis) and compared with the eigenvalues and eigenstates of a full threedimensionalSchrödinger problem corresponding to a hollow cylinder in the limitwhere the inner and outer radii approach each other. Good agreement between thetwo models is obtained for a relative difference less than 20% in inner and outerradii"
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