Conical quantum billiard revisited

Author:
Richard L. Liboff

Journal:
Quart. Appl. Math. **59** (2001), 343-351

MSC:
Primary 81Q50; Secondary 33C45, 35J25, 35Q40

DOI:
https://doi.org/10.1090/qam/1828457

MathSciNet review:
MR1828457

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Abstract: Eigenstates of a particle confined to a cone of finite length capped by a spherical surface element are derived. A countable infinite set of solutions is obtained corresponding to integer azimuthal and orbital quantum numbers . These solutions apply to a discrete subset of the domain of half vertex angles, . For arbitrary real orbital quantum numbers, , solutions are given in terms of the hypergeometric function, with , and are valid in the domain, . Eigenstates are either nondegenerate or two-fold degenerate. Numerical examples of both classes of solutions are included. For the case , the ground-state wavefunction and eigenenergy are

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Additional Information

DOI:
https://doi.org/10.1090/qam/1828457

Article copyright:
© Copyright 2001
American Mathematical Society