Algebraic study on the AN−1- and BN-Calogero models with bosonic, fermionic and distinguishable particles
نویسنده
چکیده
Abstract. Through an algebraic method using the Dunkl–Cherednik operators, the multivariable Hermite and Laguerre polynomials associated with the AN−1and BN Calogero models with bosonic, fermionic and distinguishable particles are investigated. The Rodrigues formulas of column type that algebraically generate the monic nonsymmetric multivariable Hermite and Laguerre polynomials corresponding to the distinguishable case are presented. Symmetric and anti-symmetric polynomials that respectively give the eigenstates for bosonic and fermionic particles are also presented by the symmetrization and anti-symmetrization of the non-symmetric ones. The norms of all the eigenstates for all cases are algebraically calculated in a unified way.
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