This work demonstrates the application of Bogomolny’s transfer operator method on three-dimensional dynamics. Motivated by experimental observations of lenslike metal clusters, the quantum billiards bounded by a flat bottom and an upper surface with [Formula presented] symmetry are studied. A precise determination of the energies with error less than [Formula presented] and exact predicted degeneracies in the special case of the half-sphere billiard confirm the efficiency of this method. Furthermore, the spectra and degeneracies of lens billiards with varying heights are explicitly determined.
|頁（從 - 到）||1-7|
|期刊||Physical Review E - Statistical, Nonlinear, and Soft Matter Physics|
|出版狀態||Published - 1 4月 2003|