Semiclassical quantization with short periodic orbits

We apply a recently developed semiclassical theory of short periodic orbits to the stadium billiard. We give explicit expressions for the resonances of periodic orbits and for the application of the semiclassical Hamiltonian operator to them. Then, by using the three shortest periodic orbits and two more living in the bouncing-ball region, we obtain the first 25 odd-odd eigenfunctions with surprising accuracy.