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Cluster properties of one particle Schrödinger operators. II. (English) Zbl 0920.47008

Summary: We continue the study of cluster properties of spectral and scattering characteristics of Schrödinger operators with potentials given as a sum of two wells, begun in our preceding article [Rev. Math. Phys. 6, 833-853 (1994; Zbl 0813.47011)] and where we determined the leading behaviour of the spectral shift function and the scattering amplitude as the separation of the wells tends to infinity. In this article, we determine the explicit form of the subleading contributions, which in particular show strong oscillatory behaviour. Also, we apply our methods to the critical and subcritical double well problems.

MSC:

47A40 Scattering theory of linear operators
81U20 \(S\)-matrix theory, etc. in quantum theory
47F05 General theory of partial differential operators
35J10 Schrödinger operator, Schrödinger equation

Citations:

Zbl 0813.47011
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References:

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