NDLI: Conical Quantum Billiard

Content Provider	Springer Nature Link
Author	Liboff, Richard L.
Copyright Year	1997
Abstract	The conical quantum billiard is examined. Wavefunctions are obtained in an open domain which excludes the polar axis, involving associated Legendre functions of the first and second kind. The first excited state is three-fold degenerate. One wavefunction is nonnodal. The nodal surface of either of the other states is a bisecting plane which includes the axis of the cone. These nodal properties maintain for 0 < θ$_{0}$ ≤ π/2, where θ$_{0}$ is the half vertex angle of the cone. At θ > π/2, the nonnodal state acquires a nodal at θ = π/2. Thus, as with the image problem in two dimensions, there is critical vertex angle about which the nodal structure of one of the eigenstates suffers a topological change. This nodal transition is accompanied by a geometrical transformation of the cone from convex to concave. Solutions obtained are valid for all conical quantum billiards to the limit of the spherical quantum billiard excluding the polar axis.
Starting Page	389
Ending Page	391
Page Count	3
File Format	PDF
ISSN	03779017
Journal	Letters in Mathematical Physics
Volume Number	42
Issue Number	4
e-ISSN	15730530
Language	English
Publisher	Kluwer Academic Publishers
Publisher Date	1997-01-01
Publisher Place	Dordrecht
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Group Theory and Generalizations Geometry Mathematical and Computational Physics Statistical Physics
Content Type	Text
Resource Type	Article
Subject	Statistical and Nonlinear Physics Mathematical Physics

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