Potentials producing maximally sharp resonances

Harrell, Evans M.; Svirsky, Roman

doi:10.1090/S0002-9947-1986-0816321-1

Potentials producing maximally sharp resonances
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by Evans M. Harrell and Roman Svirsky PDF

Trans. Amer. Math. Soc. 293 (1986), 723-736 Request permission

Abstract:

We consider quantum-mechanical potentials consisting of a fixed background plus an additional piece constrained only by having finite height and being supported in a given finite region in dimension $d \leqslant 3$. We characterize the potentials in this class that produce the sharpest resonances. In the one-dimensional or spherically symmetric specialization, a quite detailed description is possible. The maximally sharp resonances that we find are, roughly speaking, caused by barrier confinement of a metastable state, although in some situations they call for interactions in the interior of the confining barrier as well.

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