We present a new generalised eigenfunction of the reduced two-particle, mixed-charge, hyperbolic Ruijsenaars-Schneider (or, relativistic A_1-Calogero-Moser) Hamiltonian. The asymptotics of this function displays transmission and reflection in a way that generalizes the familiar non-relativistic picture. Using this function we construct integral transforms diagonalizing the Hamiltonian (an analytic difference operator, or A\DeltaO). When the three parametric dependences of the Hamiltonian are restricted to a certain polytope, these transforms can be used for a functional-analytic Hilbert space theory with all the desired quantum mechanical features (self-adjointness, spectrum, S-matrix etc.). As a final consideration we see how such a theory can be constructed in a different way for a special choice of the coupling parameter, with accompanying special features.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:707062 |
| Date | January 2016 |
| Creators | Haworth, Steven William |
| Contributors | Ruijsenaars, Simon |
| Publisher | University of Leeds |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Source | http://etheses.whiterose.ac.uk/16801/ |
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