Quantum section method for the soft stadium

The soft stadium is defined by a monomial potential with exponent α as a parameter, such that α→∞ corresponds to the billiard. The practical use of the quantum section method depends only on the partial separability of the system on both sides of the section, which holds for all α’s. In particular, for α=1.0, the system becomes globally separable, allowing for a general test of the method. For various values of the parameter, we also tested the use of the asymptotic WKB-type approximation in the construction of Green’s functions and asymptotic overlap integrals to obtain higher energy eigenvalues. We show these approximations to be reliable.