Affiliation:
1. Doppler Institute for Mathematical Physics and Applied Mathematics, Czech Technical University, Břehová 7, 11519 Prague, Czechia and Department of Theoretical Physics, Nuclear Physics Institute, Czech Academy of Sciences, 25068 Řež near Prague, Czechia
Abstract
We discuss a three-dimensional soft quantum waveguide, in other words, Schrödinger operator in [Formula: see text] with an attractive potential supported by an infinite tube and by keeping its transverse profile fixed. We show that if the tube is asymptotically straight, the distance between its ends is unbounded, and its twist satisfies the so-called Tang condition, the essential spectrum is not affected by smooth bends. Furthermore, we derive a sufficient condition, expressed in terms of the tube geometry, for the discrete spectrum of such an operator to be nonempty.
Funder
Grantová Agentura České Republiky
European Regional Development Fund
Subject
Mathematical Physics,Statistical and Nonlinear Physics
Cited by
3 articles.
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