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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Potentials producing maximally sharp resonances

Authors: Evans M. Harrell and Roman Svirsky
Journal: Trans. Amer. Math. Soc. 293 (1986), 723-736
MSC: Primary 81C12; Secondary 34B25, 35P05
MathSciNet review: 816321
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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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Article copyright: © Copyright 1986 American Mathematical Society