Waveguides coupled through a semitransparent barrier: A Birman-Schwinger analysis

Reviews in Mathematical Physics

Volumn 13, Issue 3, 2001, Pages 307-334

  Exner, P ^a,b   Krejcirik D ^c,d  

^a INSTITUTE OF MATHEMATICS   (Czech Republic)

^b CZECH TECHNICAL UNIVERSITY IN PRAGUE   (Czech Republic)

^c CHARLES UNIVERSITY   (Czech Republic)

^d UNIVERSITÉ DE TOULON   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0035609069     PISSN: 0129055X     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0129055X01000703     Document Type: Article

References (20)

1. Y. Avishai, D. Bessis, B. G. Giraud and G. Mantica, "Quantum bound states in open geometries", Phys. Rev. B44 (1991) 8028-8034.
2. S. Albeverio, F. Gesztesy, R. Høegh-Krohn and H. Holden, Solvable Models in Quantum Mechanics, Springer, Heidelberg, 1988.
3. J. F. Brasche, P. Exner, Yu. A. Kuperin and P. Šeba, "Schrödinger operators with singular interactions", J. Math. Anal. Appl. 184 (1994) 112-139.
4. W. Bulla, F. Gesztesy, W. Renger and B. Simon, "Weakly coupled bound states in quantum waveguides", Proc. Amer. Math. Soc. 127 (1997) 1487-1495.
5. R. Blackenbecler, M. L. Goldberger and B. Simon, "The bound states of weakly coupled long-range one-dimensional quantum Hamiltonians", Ann. Phys. 108 (1977) 69-78.
6. P. Duclos and P. Exner, "Curvature-induced bound states in quantum waveguides in two and three dimensions", Rev. Math. Phys. 7 (1995) 73-102.
7. P. Exner, R. Gawlista, P. Šeba and M. Tater, "Point interactions in a strip", Ann. Phys. 252 (1996) 133-179.
8. P. Exner and D. Krejčiřík, "Quantum waveguides with a lateral semitransparent barrier: Spectral and scattering properties", J. Phys. A32 (1999) 4475-4494.
9. P. Exner, P. Šeba, M. Tater and D. Vaněk, "Bound states and scattering in quantum waveguides coupled laterally through a boundary window", J. Math. Phys. 37 (1996) 4867-4887.
10. P. Exner and S. A. Vugalter, "Asymptotic estimates for bound states in quantum waveguides coupled laterally through a narrow window", Ann. Inst. H. Poincaré 65 (1996) 109-123.
11. P. Exner and S. A. Vugalter, "Bound states in a locally deformed waveguide: the critical case", Lett. Math. Phys. 39 (1997) 57-69.
12. T. Kato, Perturbation Theory for Linear Operators, Springer, Berlin, 1966.
13. N. Klaus, "On the bound state of Schrödinger operators in one dimension", Ann. Phys. 108 (1977) 288-300.
14. R. G. Newton, "Bounds on the number of bound states for the Schrödinger equation in one and two dimensions", J. Operator Theory 10 (1983) 119-125.
15. I. Yu. Popov, "Asymptotics of bound state for laterally coupled waveguides", Rep. Math. Phys. 43 (1999) 427-437.
16. M. M. Rao, Measure Theory and Integration, John Wiley & Sons, New York, 1987.
17. M. Reed and B. Simon, Methods of Modern Mathematical Physics, I. Functional Analysis, II. Fourier Analysis. Self-Adjointness, III. Scattering Theory, IV. Analysis of Operators, Academic Press, New York, 1972-1979.
18. N. Seto, "Bargmann's inequalities in spaces of arbitrary dimension", Publ. Res. Inst. Math. Sci. 9 (1974) 429-461.
19. B. Simon, "The bound state of weakly coupled Schrödinger operators in one and two dimensions", Ann. Phys. 97 (1976) 279-288.
20. P. Stollmann and J. Voigt, "Perturbation of Dirichlet forms by measures", Potential Analysis 5 (1996) 109-138.