Scattering and Bound State Green's Functions on a Plane via so(2,1) Lie Algebra

Details Scattering and Bound State Green's Functions on a Plane via so(2,1) Lie Algebra Scattering and Bound State Green's Functions on a Plane via so(2,1) Lie Algebra

2006-04-12

arxiv.org/abs/quant-ph/0604092v3

J.Math.Phys. 47 (2006) 112103

Physics

Quantum Physics

21 Latex pages. Typos corrected. Results unchanged. Version to appear in JMP

Scientific paper

10.1063/1.2363259

We calculate the Green's functions for the particle-vortex system, for two anyons on a plane with and without a harmonic regulator and in a uniform magnetic field. These Green's functions which describe scattering or bound states (depending on the specific potential in each case) are obtained exactly using an algebraic method related to the SO(2,1) Lie group. From these Green's functions we obtain the corresponding wave functions and for the bound states we also find the energy spectra.

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