Quasiclassical Born-Oppenheimer approximations

摘要

We discuss several problems in quasiclassical physics for which approximatesolutions were recently obtained by a new method, and which can also be solvedby novel versions of the Born-Oppenheimer approximation. These cases includethe so-called bouncing ball modes, low angular momentum states in perturbedcircular billiards, resonant states in perturbed rectangular billiards, andwhispering gallery modes. Some rare, special eigenstates, concentrated close tothe edge or along a diagonal of a nearly rectangular billiard are found. Thiskind of state has apparently previously escaped notice.