Abstract
For a class of Schrodinger operatorsH:=−(ℏ2/2m)Δ+V onL 2(ℝ n ), with potentials having minima embedded in the continuum of the spectrum and non-trapping tails, we show the existence of shape resonances exponentially close to the real axis as ℏ↘0. The resonant energies are given by a convergent perturbation expansion in powers of a parameter exhibiting the expected exponentially small behaviour for tunneling.
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