Smoothed wave functions of chaotic quantum systems
Abstract
It is shown that wave functions of quantum systems as ħ → 0 have an extra density near unstable periodic trajectories of the classical problem. The averaged wave function square is represented as the sum over a finite number of periodic trajectories. The contribution of each trajectory is expressed through the elements of the monodromy matrix of the trajectory. The results are compared with the numerical calculations of the wave functions for the stadium billiard.
- Publication:
-
Physica D Nonlinear Phenomena
- Pub Date:
- June 1988
- DOI:
- 10.1016/0167-2789(88)90075-9
- Bibcode:
- 1988PhyD...31..169B