Bound states in curved quantum waveguides

1989 ◽  
Vol 30 (11) ◽  
pp. 2574-2580 ◽  
Author(s):  
P. Exner ◽  
P. Seba
Keyword(s):  
Bound States ◽  
Quantum Waveguides

Existence of bound states in quantum waveguides under weak conditions

1995 ◽  
Vol 35 (1) ◽  
pp. 1-12 ◽  
Author(s):  
W. Renger ◽  
W. Bulla
Keyword(s):  
Bound States ◽  
Quantum Waveguides

scholarly journals Bound states in straight quantum waveguides with combined boundary conditions

2002 ◽  
Vol 43 (8) ◽  
pp. 3892-3915 ◽  
Author(s):  
J. Dittrich ◽  
J. Křı́ž
Keyword(s):  
Boundary Conditions ◽  
Bound States ◽  
Quantum Waveguides

scholarly journals Bound states and scattering in quantum waveguides coupled laterally through a boundary window

1996 ◽  
Vol 37 (10) ◽  
pp. 4867-4887 ◽  
Author(s):  
P. Exner ◽  
P. Šeba ◽  
M. Tater ◽  
D. Vaněk
Keyword(s):  
Bound States ◽  
Quantum Waveguides

scholarly journals Weakly coupled bound states in quantum waveguides

1997 ◽  
Vol 125 (5) ◽  
pp. 1487-1495 ◽  
Author(s):  
W. Bulla ◽  
F. Gesztesy ◽  
W. Renger ◽  
B. Simon
Keyword(s):  
Bound States ◽  
Weakly Coupled ◽  
Quantum Waveguides

CURVATURE-INDUCED BOUND STATES IN QUANTUM WAVEGUIDES IN TWO AND THREE DIMENSIONS

1995 ◽  
Vol 07 (01) ◽  
pp. 73-102 ◽  
Author(s):  
P. DUCLOS ◽  
P. EXNER
Keyword(s):  
Cross Section ◽  
Bound States ◽  
Bound State ◽  
Three Dimensions ◽  
Tube Radius ◽  
Dirichlet Laplacian ◽  
Bending Angle ◽  
Thin Tube ◽  
Open Questions ◽  
Quantum Waveguides

Dirichlet Laplacian on curved tubes of a constant cross section in two and three dimensions is investigated. It is shown that if the tube is non-straight and its curvature vanishes asymptotically, there is always a bound state below the bottom of the essential spectrum. An upper bound to the number of these bound states in thin tubes is derived. Furthermore, if the tube is only slightly bent, there is just one bound state; we derive its behaviour with respect to the bending angle. Finally, perturbation theory of these eigenvalues in any thin tube with respect to the tube radius is constructed and some open questions are formulated.

Bound states in tubular quantum waveguides with torsion

1996 ◽  
Vol 29 (15) ◽  
pp. 4527-4535 ◽  
Author(s):  
Iain J Clark ◽  
Anthony J Bracken
Keyword(s):  
Bound States ◽  
Quantum Waveguides
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