Absence of Quantum States Corresponding to Unstable Classical Channels

We consider Hamiltonian systems of a certain class with unstable orbits moving to infinity. We prove a theorem showing that analogous quantum states do not exist. This theorem is applied to Schrodinger operators with potentials of degree zero which are Morse when restricted to the unit sphere

Stationary scattering theory on mainifolds, I

We study spectral theory for the Schrodinger operator on manifolds possessing an escape function. A particular class of examples are manifolds with Euclidean and/or hyperbolic ends.Comment: pp 3