Weakly Coupled States on Branching Graphs

Letters in Mathematical Physics

Volumn 38, Issue 3, 1996, Pages 313-320

  Exner, Pavel ^a,b  

^a NUCLEAR PHYSICS INSTITUTE   (Czech Republic)

^b CZECH TECHNICAL UNIVERSITY IN PRAGUE   (Czech Republic)

Author keywords

Graphs; Schr dinger operators; Weak coupling

Indexed keywords

EID: 0001043689     PISSN: 03779017     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF00398355     Document Type: Article

References (20)

1. Adamyan, V. M.: Scattering matrices for microschemes, Oper. Theory: Adv. Appl. 59 (1992), 1-10.
2. Albeverio, S., Gesztesy, F., Høegh-Krohn, R. and Holden, H.: Solvable Models in Quantum Mechanics, Springer, Heidelberg, 1988.
3. Avishai, Y. and Luck, J. M.: Quantum percolation and ballistic conductance on a lattice of wires, Phys. Rev. B 45 (1992), 1074-1095.
4. Avron, J. E., Raveh, A. and Zur, B.: Adiabatic transport in multiply connected systems, Rev. Modern Phys. 60 (1988), 873-915.
5. Blanckenbecler, R., Goldberger, M. L. and Simon, B.: The bound states of weakly coupled long-range one-dimensional quantum Hamiltonians, Ann. Phys. 108 (1977), 89-78.
6. Bulla, W. and Trenckler, T.: The free Dirac operator on compact and non-compact graphs, J. Math. Phys. 31 (1990), 1157-1163.
7. Exner, P.: Lattice Kronig-Penney models, Phys. Rev. Lett. 74 (1995), 3503-3506.
8. Exner, P.: Contact interactions on graph superlattices, J. Phys. A, 29 (1996), 87-102.
9. Exner, P. and Gawlista, R.: Band spectra of rectangular graph superlattices, Phys. Rev. B, 53 (1996), No. 7.
10. Exner, P. and Šeba, P.: Free quantum motion on a branching graph, Rep. Math. Phys. 28 (1989), 7-26.
11. Gangopadhyaya, A., Pagnamenta, A. and Sukhatme, U.: Quantum mechanics of multi-prong potentials, J. Phys. A 28 (1995), 5331-5347.
12. Gerasimenko, N. I. and Pavlov, B. S.: Scattering problem on noncompact graphs, Teor. Mat. Fiz. 74 (1988), 345-359.
13. Gratus, J., Lambert, C. J., Robinson, S. J. and Tucker, R. W.: Quantum mechanics on graphs, J. Phys. A 27 (1994), 6881-6892.
14. Klaus, M.: On the bound state of Schrödinger operators in one dimension, Ann. Phys. 108 (1977), 288-300.
15. Newton, R. G.: Bounds on the number of bound states for the Schrödinger equation in one and two dimension, J. Operator Theory 10 (1983), 119-125.
16. Ruedenberg, K. and Scherr, C. W.: Free-electron network model for conjugated systems, I. Theory, J. Chem. Phys. 21 (1953), 1565-1581.
17. Seto, N.: Bargmann's inequality in spaces of arbitrary dimension, Publ. RIMS 9 (1974), 429-461.
18. Simon, B.: The bound state of weakly coupled Schrödinger operators in one and two dimensions, Ann. Phys. 97 (1976), 279-288.
19. Skriganov, M. M.: Proof of the Bethe-Sommerfeld conjecture in dimension two, Soviet Math. Dokl. 20 (1979), 956-959.
20. Skriganov, M. M.: The multidimensional Schrödinger operator with a periodic potential, Math. USSR Izvest. 22 (1984), 619-645.