Reducible boundary conditions in coupled channels

Journal of Physics A: Mathematical and General

Volumn 38, Issue 41, 2005, Pages 8979-8992

  Pankrashkin, Konstantin ^a  

^a HUMBOLDT UNIVERSITY   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 25844515792     PISSN: 03054470     EISSN: None     Source Type: Journal    
DOI: 10.1088/0305-4470/38/41/010     Document Type: Article

References (31)

1. Albeverio S, Gesztesy F, Høegh-Krohn R and Holden H 2005 Solvable Models in Quantum Mechanics 2nd edn (Providence, RI: Chelsea)
2. Wu T T and Yu M L 2002 Theory and application of Fermi pseudopotential in one dimension J. Math. Phys. 43 5949-76
3. Coutinho F A B, Nogami Y, Tomio L and Toyama F M 2004 The Fermi pseudo-potential in one dimension J. Phys. A: Math. Gen. 37 10653-63
4. Coutinho F A B, Nogami Y and Toyama F M 2004 Point interactions in one-dimensional quantum mechanics with coupled channels J. Phys. A: Math. Gen. 37 2989-97
5. Exner P and šeba P 1989 Free quantum motion on a branching graph Rep. Math. Phys. 28 7-26
6. Gerasimenko N I and Pavlov B S 1988 Scattering problems on non-compact graphs Theor. Math. Phys. 74 230-40
7. Kostrykin V and Schrader R 1999 Kirchhoff's rule for quantum wires J. Phys. A: Math. Gen. 32 595-630
8. Kuchment P 2004 Quantum graphs: I. Some basic structures Waves Random Media 14 S107-28
9. Pavlov B S 1987 The theory of extensions and explicitly-solvable models Russ. Math. Surv. 42 127-68
10. šeba P 1986 The generalized point interaction in one dimension Czech. J. Phys. 36 667-73
11. Chernoff P and Hughes R 1993 A new class of point interactions in one dimension J. Funct. Anal. 111 97-117
12. Albeverio S, Dabrowski L and Kurasov P 1998 Symmetries of Schrödinger operators with point interactions Lett. Math. Phys. 45 33-47
13. Boman J and Kurasov P 2005 Symmetries of quantum graphs and the inverse scattering problem Adv. Appl. Math. 35 58-70
14. Kurasov P and Nowaczyk M 2005 Inverse spectral problem for quantum graphs J. Phys. A: Math. Gen. 38 4901-15
15. Cheon T and Exner P 2004 An approximation to δ′-couplings on graphs J. Phys. A: Math. Gen. 37 L329-35
16. Rofe-Beketov F S 1969 Self-adjoint extensions of differential operators in a space of vector-valued functions Sov. Math. Dokl. 184 1034-7
17. Brüning J and Geyler V A 2003 Scattering on compact manifolds with infinitely thin horns J. Math. Phys. 44 371-405
18. Harmer M 2000 Hermitian symplectic geometry and extension theory J. Phys. A: Math. Gen. 33 9193-203
19. Gorbachuk V I and Gorbachuk M L 1991 Boundary Value Problems for Operator Differential Equations (Dordrecht: Kluwer)
20. Mikhailets V A and Sobolev A V 1999 Common eigenvalue problem and periodic Schrödinger operators J. Funct. Anal. 165 150-72
21. Albeverio S and Pankrashkin K 2005 A remark on Krein's resolvent formula and boundary conditions J. Phys. A: Math. Gen. 38 4859-64
22. Exner P 1996 Contact interactions on graph superlattices J. Phys. A: Math. Gen. 29 87-102
23. Exner P and Post O 2005 Convergence of spectra of graph-like thin manifolds J. Geom. Phys. 54 77-115
24. Albeverio S and Kurasov P 2000 Singular Perturbations of Differential Operators. Solvable Schrödinger Type Operators (Cambridge: Cambridge University Press)
25. Kuchment P 2005 Quantum graphs: II. Some spectral properties of quantum and combinatorial graphs J. Phys. A: Math. Gen. 38 4887-900
26. Oleinik V, Pavlov B and Sibirev N 2004 Analysis of the dispersion equation for the Schrödinger operator on periodic metric graphs Waves Random Media 14 157-83
27. Hughes R 1998 Generalized Kronig-Penney Hamiltonians J. Math. Anal. Appl. 222 151-66
28. Kurasov P and Larson J 2002 Spectral asymptotics for Schrödinger operators with periodic point interactions J. Math. Anal. Appl. 266 127-48
29. Cheon T and Shigehara T 2004 Continuous spectra of generalized Kronig-Penney model J. Phys. Soc. Japan 73 2986-90
30. Carlson R 2004 Spectral theory and spectral gaps for periodic Schrödinger operators on product graphs Waves Random Media 14 S29-45
31. Oleinik V and Pavlov B 2003 Embedded spectrum on a metric graph (an observation) Zap. Nauchn. Sem. St.-Peterburg. Otdel. Mat. Inst. Steklov (POMI) 300 215-20