We derive a functional equation for the Fredholm determinant of the boundary element method. By assuming that the functional equation holds for the semiclassical Fredholm determinant for strongly chaotic billiards, we obtain a real function whose zeros are the semiclassical eigenenergies. We also show by the numerical experiment of concave triangle billiards that the semiclassical eigenenergies are very close to the exact eigenenergies.
ASJC Scopus subject areas
- Physics and Astronomy (miscellaneous)