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Effective Hamiltonians for thin Dirichlet tubes with varying cross-section. (English) Zbl 1238.81100

Exner, Pavel (ed.), Mathematical results in quantum physics. Proceedings of the QMath11 conference, Hradec Králové, Czech Republc, September 6–10, 2010. Special session in honour of Ari Laptev. With DVD-ROM. Hackensack, NJ: World Scientific (ISBN 978-981-4350-35-8/hbk; 978-981-4350-36-5/ebook). 183-189 (2011).
Summary: We show how to translate recent results on effective Hamiltonians for quantum systems constrained to a submanifold by a sharply peaked potential to quantum systems on thin Dirichlet tubes. While the structure of the problem and the form of the effective Hamiltonian stays the same, the difficulties in the proofs are different.
For the entire collection see [Zbl 1234.81016].

MSC:

81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics
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