New nonsymmetric orthogonal basis for the Calogero model with distinguishable particles
نویسندگان
چکیده
منابع مشابه
New Non-Symmetric Orthogonal Basis for the Calogero Model with Distinguishable Particles
We demonstrate an algebraic construction of all the simultaneous eigenfunctions of the conserved operators for distinguishable particles governed by the Calogero Hamiltonian. Our construction is completely parallel to the construction of the Fock space for decoupled quantum harmonic oscillators. The simultaneous eigenfunction does not coincide with the non-symmetric Hi-Jack polynomial, which sh...
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Abstract. Integrability, algebraic structures and orthogonal basis of the Calogero model are studied by the quantum Lax and Dunkl operator formulations. The commutator algebra among operators including conserved operators and creation-annihilation operators has the structure of the W-algebra. Through an algebraic construction of the simultaneous eigenfunctions of all the commuting conserved ope...
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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...
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Abstract. The Calogero model is a one-dimensional quantum integrable system with inverse-square long-range interactions confined in an external harmonic well. It shares the same algebraic structure with the Sutherland model, which is also a one-dimensional quantum integrable system with inverse-sine-square interactions. Inspired by the Rodrigues formula for the Jack polynomials, which form the ...
متن کاملBogoliubov Transformation for Distinguishable Particles
The Bogoliubov transformation is generally derived in the context of identical bosons with the use of " second quantized " a and a † operators (or, equivalently, in field theory). Here, we show that the transformation , together with its characteristic energy spectrum, can also be derived within the Hilbert space of distinguishable particles, obeying Boltzmann statistics; in this derivation, or...
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ژورنال
عنوان ژورنال: Physics Letters A
سال: 1998
ISSN: 0375-9601
DOI: 10.1016/s0375-9601(98)00769-5