Quantum ergodicity at a finite energy level
The author considers classical homogeneous Hamilton flows which commute with \(R_+\)-action on the cotangent bundle. A notion of quantum ergodicity at a finite energy level for the quantum mechanics corresponding to such systems is formulated. The relationship between quantum and classical ergodicity is investigated. Under some assumptions on the classical system the author obtains necessary and sufficient conditions in terms of semi-classical asymptotic behavior of eigenfunctions of a quantum Hamiltonian.
scientific article; zbMATH DE number 1398930
scientific article