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 / Ph. D.
| Identifer | oai:union.ndltd.org:VTETD/oai:vtechworks.lib.vt.edu:10919/53936 |
| Date | January 1988 |
| Creators | Clemence, Dominic Pharaoh |
| Contributors | Mathematics, Klaus, Martin, Shaw, J.K., Ball, Joseph A., Thomson, J.E., Herdman, Terry L., Wheeler, Robert |
| Publisher | Virginia Polytechnic Institute and State University |
| Source Sets | Virginia Tech Theses and Dissertation |
| Language | en_US |
| Detected Language | English |
| Type | Dissertation, Text |
| Format | v, 80 leaves, application/pdf, application/pdf |
| Rights | In Copyright, http://rightsstatements.org/vocab/InC/1.0/ |
| Relation | OCLC# 19736111 |
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