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A quantum dot with impurity in the Lobachevsky plane. (English) Zbl 1158.81334
Behrndt, Jussi (ed.) et al., Spectral theory in inner product spaces and applications. Papers of the 6th workshop on operator theory in Krein spaces and operator polynomials, TU Berlin, Germany, December 14–17, 2006. Basel: Birkhäuser (ISBN 978-3-7643-8910-9/hbk). Operator Theory: Advances and Applications 188, 135-148 (2009).
Summary: The curvature effect on a quantum dot with impurity is investigated. The model is considered on the Lobachevsky plane. The confinement and impurity potentials are chosen so that the model is explicitly solvable. The Green function as well as the Krein $$Q$$-function are computed.
For the entire collection see [Zbl 1151.47002].

##### MSC:
 81Q37 Quantum dots, waveguides, ratchets, etc. 81Q15 Perturbation theories for operators and differential equations in quantum theory 82D20 Statistical mechanical studies of solids 81Q10 Selfadjoint operator theory in quantum theory, including spectral analysis
##### Keywords:
quantum dot; Lobachevsky plane; point interaction; spectrum
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