Functional model for extensions of symmetric operators and applications to scattering theory. (English) Zbl 07006654
Summary: On the basis of the explicit formulae for the action of the unitary group of exponentials corresponding to almost solvable extensions of a given closed symmetric operator with equal deficiency indices, we derive a new representation for the scattering matrix for pairs of such extensions. We use this representation to explicitly recover the coupling constants in the inverse scattering problem for a finite non-compact quantum graph with \(\delta\)-type vertex conditions.
MSC:
| 47A45 | Canonical models for contractions and nonselfadjoint linear operators |
| 34L25 | Scattering theory, inverse scattering involving ordinary differential operators |
| 81Q35 | Quantum mechanics on special spaces: manifolds, fractals, graphs, lattices |
Keywords:
functional model; extensions of symmetric operators; boundary triples; inverse scattering problemsReferences:
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