Symmetric Fock space and orthogonal symmetric polynomials associated with the Calogero model

DOI10.1016/S0960-0779(98)00138-6zbMath1002.81012arXivcond-mat/9803284MaRDI QIDQ1573917

Hideaki Ujino, Miki Wadati, Akinori Nishino

Publication date: 9 August 2000

Published in: Chaos, Solitons and Fractals (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/cond-mat/9803284

zbMATH Keywords

similarity transformationJack polynomialbosonic statedecoupled quantum harmonic oscillatorsDunkl operator formulationsimultaneous eigenfunctions

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Many-body theory; quantum Hall effect (81V70) Confluent hypergeometric functions, Whittaker functions, ({}_1F_1) (33C15)

Related Items (4)

Pseudo-bosons for the \(D_2\) type quantum Calogero model ⋮ \(W_{1+\infty}\) constraints for the Hermitian one-matrix model ⋮ CFT approach to constraint operators for (\(\beta\)-deformed) Hermitian one-matrix models ⋮ Exact solution of D N-type quantum Calogero model through a mapping to free harmonic oscillators

Cites Work

• The Calogero-Sutherland model and generalized classical polynomials
• Confluent hypergeometric orthogonal polynomials related to the rational quantum Calogero system with harmonic confinement
• Fractional statistics in one dimension: View from an exactly solvable model
• Some combinatorial properties of Jack symmetric functions
• Algebraic approach to the eigenstates of the quantum Calogero model confined in an external harmonic well
• Exact operator solution of the Calogero-Sutherland model
• Multicomponent Calogero model of \(B_N\)-type confined in a harmonic potential
• The Calogero model---anyonic representation, fermionic extension and supersymmetry
• New nonsymmetric orthogonal basis for the Calogero model with distinguishable particles
• Differential-Difference Operators Associated to Reflection Groups
• An orthogonal basis for the -type Calogero model
• Algebraic Construction of a New Symmetric Orthogonal Basis for the Calogero Model
• Orthogonality of the Hi-Jack Polynomials Associated with the Calogero Model
• Rodrigues Formula for Hi-Jack Symmetric Polynomials Associated with the Quantum Calogero Model
• A Simple Derivation of Multivariable Hermite and Legendre Polynomials
• Algebraic Construction of the Eigenstates for the Second Conserved Operator of the Quantum Calogero Model
• Orthogonal Symmetric Polynomials Associated with the Quantum Calogero Model
• The Quantum Calogero Model and theW-Algebra
• Exchange operator formalism for integrable systems of particles
• Erratum: Solution of the one-dimensional N-body problems with quadratic and/or inversely quadratic pair potentials [J. Math. Phys. 12, 419–436 (1971)]
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