Exchange operator formalism for an infinite family of solvable and integrable quantum systems on a plane
201010 pages
Published in:
- Mod.Phys.Lett.A 25 (2010) 15-24
e-Print:
- 0910.2151 [math-ph]
Report number:
- ULB-229-CQ-09-3
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Abstract: (WSP)
The exchange operator formalism in polar coordinates, previously considered for the Calogero-Marchioro-Wolfes problem, is generalized to a recently introduced, infinite family of exactly solvable and integrable Hamiltonians Hk, k = 1, 2, 3,\dots, o n a plane. The elements of the dihedral group D2k are realized as operators on this plane and used to define some differential-difference operators Dr and Dphi. The latter serve to construct D2k-extended and invariant Hamiltonians , from wh ich the starting Hamiltonians Hk can be retrieved by projection in the D2k identity representation space.Note:
- 12 pages, no figure; minor changes; published version
- 03.65.Fd
- Quantum Hamiltonians
- integrability
- exchange operators
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