Use this URL to cite or link to this record in EThOS:
Title: Spectral properties of integrable Schrodinger operators with singular potentials
Author: Haese-Hill, William
ISNI:       0000 0004 5372 4133
Awarding Body: Loughborough University
Current Institution: Loughborough University
Date of Award: 2015
Availability of Full Text:
Access from EThOS:
Access from Institution:
The integrable Schrödinger operators often have a singularity on the real line, which creates problems for their spectral analysis. In several particular cases we show that all closed gaps lie on the infinite spectral arc. In the second part we develop a theory of complex exceptional orthogonal polynomials corresponding to integrable rational and trigonometric Schrödinger operators, which may have a singularity on the real line. In particular, we study the properties of the corresponding complex exceptional Hermite polynomials related to Darboux transformations of the harmonic oscillator, and exceptional Laurent orthogonal polynomials related to trigonometric monodromy-free operators.
Supervisor: Not available Sponsor: EPSRC
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: Complex Lame´ operators ; Monodromy-free Schro¨dinger operators ; Exceptional orthogonal polynomials