1. Solutions of the Lippmann-Schwinger equation for confocal parabolic billiards
- Author
-
Ruiz-Biestro, Alberto and Gutierrez-Vega, Julio C.
- Subjects
Quantum Physics ,Physics - Computational Physics ,Physics - Optics - Abstract
We present analytical and numerical solutions of the Lippmann-Schwinger equation for the scattered wavefunctions generated by confocal parabolic billiards and parabolic segments with various $\delta$-type potential-strength functions. The analytical expressions are expressed as summations of products of parabolic cylinder functions $D_m$. We numerically investigate the resonances and tunneling in the confocal parabolic billiards by employing an accurate boundary wall method that provides a complete inside-outside picture. The criterion for discretizing the parabolic sides of the billiard is explained in detail. We discuss the phenomenon of transparency at certain eigenenergies., Comment: 16 pages, 14 figures
- Published
- 2023
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