Resonance expansions of propagators in the presence of potential barriers

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Abstract

We show that the Schrödinger propagator can be expanded in terms of resonances at energy levels at which a barrier separates the interaction region from infinity. The expansions hold for all times with errors small in the semi-classical parameter. As a byproduct we obtain a result on the approximation of clusters of resonant states by clusters of eigenfunctions of a self-adjoint reference operator.

MSC

Primary: 35Q40
Secondary: 35B40
47F05
81U05

Keywords

Quantum resonances
Long time behavior of solutions
Semi-classical expansions

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