Widely Separated Deformations of Singular Potential
Institute of Physics, University of Zielona Góra,
ul. Szafrana 4a, 65-246 Zielona Góra, Poland
e-mail: skondej@proton.if.uz.zgora.pl
Received:
Received: 23 March 2010; accepted 8 July 2010; published online: 6 September 2010
DOI: 10.12921/cmst.2010.16.02.162-167
OAI: oai:lib.psnc.pl:725
Abstract:
We study the two dimensional quantum system governedby the Schrödinger operator with delta type potential. The interaction is supported by line Γ which coincides with a straight at infinity and which admits two widely separated deformations. The aim of this paper is to express the number of bound states of our system by the number of bound states of the system with single deformation.
Key words:
References:
[1] S. Albeverio, F. Gesztesy, R. Høegh-Krohn, H. Holden, Solvable Models in Quantum Mechanics. 2nd printing (with Appendix by P. Exner), AMS, Providence, R.I. (2004).
[2] P. Exner, T. Ichinose, Geometrically induced spectrum in curved leaky wires. J. Phys. A34, 1439-1450 (2001).
[3] P. Exner, S. Kondej, Scattering by local deformations of a straight leaky wire. J. Phys. A38, 4865-4874 (2005).
[4] J. Cisło, S. Kondej, Upper bound for the number of bound states induced by the curvature of singular potential. submitted.
[5] J.F. Brasche, P. Exner, Yu.A. Kuperin, P. Šeba, Schrödinger operators with singular interactions. J. Math. Anal. Appl. 184, 112-139 (1994).
We study the two dimensional quantum system governedby the Schrödinger operator with delta type potential. The interaction is supported by line Γ which coincides with a straight at infinity and which admits two widely separated deformations. The aim of this paper is to express the number of bound states of our system by the number of bound states of the system with single deformation.
Key words:
References:
[1] S. Albeverio, F. Gesztesy, R. Høegh-Krohn, H. Holden, Solvable Models in Quantum Mechanics. 2nd printing (with Appendix by P. Exner), AMS, Providence, R.I. (2004).
[2] P. Exner, T. Ichinose, Geometrically induced spectrum in curved leaky wires. J. Phys. A34, 1439-1450 (2001).
[3] P. Exner, S. Kondej, Scattering by local deformations of a straight leaky wire. J. Phys. A38, 4865-4874 (2005).
[4] J. Cisło, S. Kondej, Upper bound for the number of bound states induced by the curvature of singular potential. submitted.
[5] J.F. Brasche, P. Exner, Yu.A. Kuperin, P. Šeba, Schrödinger operators with singular interactions. J. Math. Anal. Appl. 184, 112-139 (1994).
