New nonsymmetric orthogonal basis for the Calogero model with distinguishable particles. (English) Zbl 0941.81058
Summary: The authors demonstrate an algebraic construction of all the simultaneous eigenfunctions of the conserved operators for distinguishable particles governed by the Calogero Hamiltonian. This construction is completely parallel to the construction of the Fock space for decoupled quantum harmonic oscillators. The simultaneous eigenfunction does not coincide with the nonsymmetric Hi-Jack polynomial, which shows that the conserved operators derived from the number operators of the decoupled quantum harmonic oscillators are algebraically different from the known ones derived by the Dunkl operator formulation.
MSC:
| 81V70 | Many-body theory; quantum Hall effect |
| 33D80 | Connections of basic hypergeometric functions with quantum groups, Chevalley groups, \(p\)-adic groups, Hecke algebras, and related topics |
| 37K10 | Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) |
Keywords:
nonsymmetric orthogonal basis; simultaneous eigenfunctions; conserved operators; Calogero Hamiltonian; nonsymmetric Hi-Jack polynomialReferences:
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