Microwave experiments on chaotic billiards

We describe experiments using billiard-shaped microwave cavities, to test ideas in quantum chaos. The experimental method for observing cavity resonances to obtain the eigenvalues, and the advantages and limitations of the techniques, including the influence of absorption, are discussed. An experimental technique to obtain a 2D mapping of the wavefunction is described. Results are displayed for 36 of the low-lying wavefunctions of a Sinai billiard cavity consisting of a central disc in a rectangular enclosure. The wavefunctions demonstrate the influence of classical periodic orbits (PO), of which there are two types: non-isolated PO, which avoid the central disc, and isolated PO, which hit the central disc. Scarred states, including those associated with isolated PO, are directly observed.