Scattering matrices and Weyl functions∗
نویسندگان
چکیده
For a scattering system {AΘ, A0} consisting of selfadjoint extensions AΘ and A0 of a symmetric operator A with finite deficiency indices, the scattering matrix {SΘ(λ)} and a spectral shift function ξΘ are calculated in terms of the Weyl function associated with the boundary triplet for A∗ and a simple proof of the Krein-Birman formula is given. The results are applied to singular Sturm-Liouville operators with scalar and matrix potentials, to Dirac operators and to Schrödinger operators with point interactions. ∗This work was supported by DFG, Grant 1480/2
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ar X iv : m at h - ph / 0 60 40 13 v 1 6 A pr 2 00 6 Scattering matrices and Weyl functions ∗
For a scattering system {AΘ, A0} consisting of selfadjoint extensions AΘ and A0 of a symmetric operator A with finite deficiency indices, the scattering matrix {SΘ(λ)} and a spectral shift function ξΘ are calculated in terms of the Weyl function associated with the boundary triplet for A∗ and a simple proof of the Krein-Birman formula is given. The results are applied to singular Sturm-Liouvill...
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تاریخ انتشار 2006