Classical system underlying a diffracting quantum billiard

Abstract

For a point scatterer placed slightly off the centre of a circular enclosure, rays are found which vividly exhibit the effect of diffraction. The Schrodinger equation was mapped in the complex plane by employing a fractional linear transformation which brings the point scatterer to the centre. But the mass of the particle becomes a function of space coordinates, bearing anisotropy. For the transformed problem, the corresponding classical Hamiltonian is written and solved with Snell’s laws on the boundary. The solutions of the Hamilton’s equations thus found constitute, in fact, the ray-manifold underlying the diffraction at the level of the wave description.