In this talk I will give an overview of Seba's billiard as a popular model in the field of Quantum Chaos. Consider a rectangular billiard with a Dirac mass placed in its interior. Whereas this mass has essentially no effect on the classical dynamics, it does have an effect on the quantum dynamics, because quantum wave packets experience diffraction at the point obstacle. Numerical investigations of this model by Petr Seba suggested that the spectrum and the eigenfunctions of the Seba billiard resemble the spectra and eigenfunctions of billiards which are classically chaotic.
I will give an introduction to this model and discuss recent results on quantum ergodicity, superscars and the validity of Berry's random wave conjecture. This talk is based on joint work with Par Kurlberg and Zeev Rudnick.