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Soft quantum waveguides in three dimensions
- 1.0557578 - ÚJF 2023 RIV US eng J - Journal Article
Exner, Pavel
Soft quantum waveguides in three dimensions.
Journal of Mathematical Physics. Roč. 63, č. 4 (2022), č. článku 042103. ISSN 0022-2488. E-ISSN 1089-7658
R&D Projects: GA ČR(CZ) GA21-07129S
Institutional support: RVO:61389005
Keywords : waveguides * Schrodinger operator
OECD category: Pure mathematics
Impact factor: 1.3, year: 2022
Method of publishing: Limited access
https://doi.org/10.1063/5.0069284
We discuss a three-dimensional soft quantum waveguide, in other words, Schrodinger operator in R-3 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.
Permanent Link: http://hdl.handle.net/11104/0331539
Number of the records: 1