Gravesen J., Willatzen M. — Schrödinger problems for surfaces of revolution—the finite cylinder as a test example
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Название: Schrödinger problems for surfaces of revolution—the finite cylinder as a test example
Авторы: Gravesen J., Willatzen M.
Аннотация:
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 threedimensional
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
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