Quantum circular billiards: Further analytical results

Author-Highlights
• A two-term recursion for mean values of powers of radial coordinate is given.
• A three-term recursion for mean values of powers of momentum is given.
• Analytical expressions for these mean values are given.
• Wave functions and orthogonality relations in momentum space are given.
• Comparison of these quantum results with classical ones is achieved.

Analytical results for circular billiards are obtained for different quantities. In particular a two-term recursion relation for mean values of powers of radial coordinate is given and a three-term recursion relation for mean values of powers of total momentum is given. Analytical expressions for these mean values are also determined, and briefly compared with the results of classical mechanics.