Electronic Resource
College Park, Md.
:
American Institute of Physics (AIP)
Journal of Mathematical Physics
35 (1994), S. 2218-2228
ISSN:
1089-7658
Source:
AIP Digital Archive
Topics:
Mathematics
,
Physics
Notes:
The circular-sector quantum-billiard problem is studied. Numerical evaluation of the zeros of first-order Bessel functions finds that there is an abrupt change in the nodal-line structure of the first excited state of the system (equivalently, second eigenstate of the Laplacian) at the critical sector-angle θc=0.354π. For sector-angle θ0, in the domain 0〈θ0〈θc, the nodal curve of the first excited state is a circular-arc segment. For θc〈θ0≤π, the nodal curve of the first excited state is the bisector of the sector. Otherwise nondegenerate first excited states become twofold degenerate at the critical-angle θc. The ground- and first-excited-state energies (EG,E1) increase monotonically as θ0 decreases from its maximum value, π. A graph of E1 vs θ0 reveals an inflection point at θ0=θc, which is attributed to the change in Bessel-function contribution to the development of E1. A proof is given for the existence of a common zero for two Bessel functions whose respective orders differ by a noninteger. Application of these results is made to a number of closely allied quantum-billiard configurations.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1063/1.530547
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