Abstract
In the mathematical theory of scattering processes the condition that certain pertinent operators are of trace-class plays a central role. For instance, it is shown by Kato [1], Birman and Krein [2] and others that a sufficient condition for the existence, completeness and the “invariance property” of the Möller wave operators is that the difference \(R_z - R_z^0 \) of the resolvents of the total and the unperturbed Hamiltonians is of trace-class (or more generally \(R_z^n - R_z^{0n} \) is of trace-class for some integer n).
Partially supported by the Swiss National Science Foundation.
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References
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© 1974 D. Reidel Publishing Company, Dordrecht-Holland
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Martin, P., Misra, B. (1974). A Refinement of the Kato-Rosenblum Lemma and Its Applications in Scattering Theory: Relativistic Potential Scattering, High Energy Behaviour of Scattering Cross Sections and the Time-Delay Operator. In: Lavita, J.A., Marchand, JP. (eds) Scattering Theory in Mathematical Physics. NATO Advanced Study Institutes Series, vol 9. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-2147-0_9
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