Bound states and scattered states for contraction semigroups |
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Authors: | Goldstein Jerome A |
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Institution: | (1) Department of Mathematics and Quantum Theory Group, Tulane University, 70118 New Orleans, LA, U.S.A. |
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Abstract: | LetA generate a strongly continuous contraction semigroup {T(t)} on a Hilbert space and letL be a bounded operator. IfL(ζI−A)−1 is compact, then the Cesàro limit of ‖LT(t)f‖2 (ast→∞) is computed for all vectorsf. This limit is interpreted in terms of bound and scattered states in the context of quantum mechanical and classical wave
propagation problems.
Partially supported by a NSF grant. |
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Keywords: | Primary 47D05 secondary 34G10 35P25 47D45 |
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