Half-bound states of a one-dimensional Dirac system: their effect on the Titchmarsh-Weyl M([lambda])-function and the scattering matrix

We study the effect of the so-called half-hound states on the Titchmarsh-Weyl M(λ)· function and the S-matrix for a one dimensional Dirac system. For short range potentials with finite first (absolute) moments, we gave an M(λ) characterization of half bound states and, as a corollary, we deduce the behavior of the spectral function near the spectral gap endpoints. Further, we establish community of the S-matrix in momentum space and prove the Levinson theorem as a corollary to this analysis. We also obtain explicit asymptotics of the S-matrix for power-law potentials

Name thesis:degree_name

Ph. D.

Level thesis:degree_level

doctoral

Discipline thesis:degree_discipline

Mathematics

Department dc:contributor.department

Mathematics

Grantor dc:publisher

Virginia Polytechnic Institute and State University

Year dc:date.issued

1988

Author dc:creator

• Clemence, Dominic Pharaoh

Chair dc:contributor.committeechair

• Klaus, Martin

Committee members dc:contributor.committeemember

• Shaw, J.K.
• Ball, Joseph A.
• Thomson, J.E.
• Herdman, Terry L.
• Wheeler, Robert

Statement dc:rights

• In Copyright

Licence dc:rights.uri

• http://rightsstatements.org/vocab/InC/1.0/

Language dc:language.iso

en_US

Handle dc:identifier.uri

http://hdl.handle.net/10919/53936

OAI identifier oai:identifier

oai:vtechworks.lib.vt.edu:10919/53936