Quantum mechanics of the two-dimensional circular billiard plus baffle system and half-integral angular momentum

We examine the quantum mechanical eigensolutions of the two-dimensional infinite-well or quantum billiard system consisting of a circular boundary with an infinite barrier or baffle along a radius. Because of the change in boundary conditions, this system includes quantized angular momentum values corresponding to half-integral multiples of ℏ/2. We discuss the resulting energy eigenvalue spectrum and visualize some of the novel energy eigenstates found in this system. We also discuss the density of energy eigenvalues, N(E), comparing this system to the standard circular well. These two billiard geometries have the same area (A = πR²), but different perimeters (P = 2πR versus (2π + 2)R), and we compare both cases to fits of N(E) which make use of purely geometric arguments involving only A and P. We also point out connections between the angular solutions of this system and the familiar pedagogical example of the one-dimensional infinite-well plus δ-function potential.