Wavefunctions, expectation values and scars on Poincare sections - A scattering approach

Using the scattering approach to quantization, we define an appropriate representation of the billiard wavefunction on the scattering Poincare section. The expectation values of smooth operators in terms of these Poincare section wavefunctions are expressed as sums over periodic orbits. A special operator is used to define scars on the section and the relation to scars in configuration space is discussed and demonstrated numerically.