Absence of Quantum States Corresponding to Unstable Classical Channels

Abstract

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.

References in corpus (1)

• Classical and quantum dynamics for 2D-electromagnetic potentials asymptotically homogeneous of degree zero

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