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 . 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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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1986-0816321-1

Article copyright:
© Copyright 1986
American Mathematical Society