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Title: Analysis of Regge poles in non-relativistic quantum mechanics
Author: Hiscox, Aaron
ISNI:       0000 0004 2751 5266
Awarding Body: Cardiff University
Current Institution: Cardiff University
Date of Award: 2011
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Regge poles—the name given to poles of the scattering amplitude in the complex angular momentum plane—are of utmost importance in atomic and molecular scattering. We investigate various aspects of non-relativistic Regge pole theory, namely, their behaviour at low energy, cardinality, and sensitivity to boundary conditions. upon investigation of the former, we find the long-standing conjecture that Regge poles become stable bound states for ultra low energy to be true; the proof is achieved for a potential satisfying the first moment condition at infinity and whose product with the radial variable is bounded near the origin, with the proviso that singular behaviour of the Regge poles may occur. It is known that for an analytic potential V with r2|V(r)| bounded at the origin and at infinity, there are finitely many Regge poles; we demonstrate that this is still the case for a compactly supported potential which is not as singular as the Coulomb interaction at the origin. This begs the question of whether or not it is possible to explicitly count Regge poles. Not only is this a difficult and interesting mathematical problem, but it also has implications in atomic physics where total cross-sections are often calculated using summations over Regge pole contributions. The author’s attempt at counting Regge poles has revealed an unexpected effect on the Regge poles due to boundary conditions: we show that infinitely many Regge poles go to infinity under nothing more than a change of boundary condition, at least for the free particle case.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available