Exact operator solution of the Calogero-Sutherland model

Abstract

The wave functions of the Calogero-Sutherland model are known to be expressible in terms of Jack polynomials. A formula which allows to obtain the wave functions of the excited states by acting with a string of creation operators on the wave function of the ground state is presented and derived. The creation operators that enter in this formula of Rodrigues-type for the Jack polynomials involve Dunkl operators.

35 pages, LaTeX2e with amslatex

References in corpus (2)

• Excited States of Calogero-Sutherland Model and Singular Vectors of the $W_N$ Algebra
• A Rodrigues formula for the Jack polynomials and the Macdonald-Stanley conjecture

Cited by in corpus (117)

• The Calogero-Sutherland Model and Generalized Classical Polynomials
• Physics and Mathematics of Calogero particles
• A recursion and a combinatorial formula for Jack polynomials
• Quantum $W_N$ Algebras and Macdonald Polynomials
• Hidden Algebras of the (super) Calogero and Sutherland models
• Equivalence of the Calogero-Sutherland Model to Free Harmonic Oscillators
• Calogero-Moser Models V: Supersymmetry and Quantum Lax Pair
• Quantum Calogero-Moser Models: Integrability for all Root Systems
• Common Algebraic Structure for the Calogero-Sutherland Models
• Conformal blocks in Virasoro and W theories: duality and the Calogero-Sutherland model
• Exact Solutions of the 2D Dunkl--Klein--Gordon Equation: The Coulomb Potential and the Klein--Gordon Oscillator
• Exact Solution of the Relativistic Dunkl Oscillator in $(2+1)$ Dimensions
• Dunkl-Klein-Gordon equation in three-dimensions: The Klein-Gordon oscillator and Coulomb Potential
• Supersymmetric Calogero-Moser-Sutherland models and Jack superpolynomials
• Rodrigues Formula for Hi-Jack Symmetric Polynomials Associated with the Quantum Calogero Model
• Algebraic approach for the one-dimensional Dirac-Dunkl oscillator
• Thermal Properties of Relativistic Dunkl Oscillators
• $SU(1,1)$ solution for the Dunkl-Coulomb problem in two dimensions and its coherent states
• Families of superintegrable Hamiltonians constructed from exceptional polynomials
• A_N-type Dunkl operators and new spin Calogero-Sutherland models
• Dunkl-Graphene in constant magnetic field
• Exact solutions of the Schrödinger Equation with Dunkl Derivative for the Free-Particle Spherical Waves, the Pseudo-Harmonic Oscillator and the Mie-type Potential
• Supersymmetric Quantum Mechanics with Reflections
• Orthogonality of Jack polynomials in superspace
• Landau levels for the $(2+1)$ Dunkl-Klein-Gordon oscillator
• Ideal Bose Gas and Blackbody Radiation in the Dunkl Formalism
• Shape Invariance in the Calogero and Calogero-Sutherland Models
• The Bannai-Ito algebra and a superintegrable system with reflections on the 2-sphere
• Exact solutions of an elliptic Calogero--Sutherland model
• Quantum propagation across cosmological singularities
• From $s{l}_q(2)$ to a Parabosonic Hopf Algebra
• Jack polynomials in superspace
• Rationally-extended Dunkl oscillator on the line
• The condensation of ideal Bose gas in a gravitational field in the framework of Dunkl-statistic
• Dunkl-Pauli Equation in the Presence of a Magnetic Field
• $q$-Analogue of the Dunkl transform on the real line
• A unified construction of generalised classical polynomials associated with operators of Calogero-Sutherland type
• Effect of the two-parameter generalized Dunkl derivative on the two-dimensional Schrödinger equation
• Sekiguchi-Debiard operators at infinity
• Superanalogs of the Calogero operators and Jack polynomials
• Interacting Particles on the Line and Dunkl Intertwining Operator of Type A: Application to the Freezing Regime
• Generalized Hermite polynomials in superspace as eigenfunctions of the supersymmetric rational CMS model
• Free harmonic oscillators, Jack polynomials and Calogero-Sutherland systems
• On the Sutherland Spin Model of B_N Type and its Associated Spin Chain
• Quantum Integrable Systems from Conformal Blocks
• New Algebraic Quantum Many-body Problems
• Generalized Calogero model in arbitrary dimensions
• Dunkl-Schrödinger equation with time-dependent harmonic oscillator potential
• Degeneracy Structure of the Calogero-Sutherland Model: an Algebraic Approach
• Time-Dependent Dunkl-Schrödinger Equation with an Angular-Dependent Potential
• Dunkl-Schrodinger Equation in Higher Dimension
• A Unified Algebraic Approach to Few and Many-Body Correlated Systems
• The Condensation of Ideal Dunkl-Bose Gas in Power-Law Traps
• Solvable scalar and spin models with near-neighbors interactions
• The dual of the Hardy space associated with the Dunkl operators
• Eigenvalues of Ruijsenaars-Schneider models associated with $A_{n-1}$ root system in Bethe ansatz formalism
• One-dimensional Dunkl Quantum Mechanics: A Path Integral Approach
• On Dunkl-Bose-Einstein Condensation in Harmonic Traps
• Rodrigues Formula for the Nonsymmetric Multivariable Hermite Polynomial
• Dynamical symmetry algebra of the Calogero model
• Sonine Transform Associated to the Dunkl Kernel on the Real Line
• Non-Hermitian boost deformation
• An infinite family of superintegrable Hamiltonians with reflection in the plane
• Calogero-Sutherland Particles as Quasisemions
• Multiple algebraisations of an elliptic Calogero-Sutherland model
• Time delay statistics for finite number of channels in all symmetry classes
• Non-Hermitian Oscillator and R-deformed Heisenberg Algebra
• Rodrigues Formula for the Nonsymmetric Multivariable Laguerre Polynomial
• One-Dimensional Quantum Systems with Ground-State of Jastrow Form Are Integrable
• Exact coherent states in one-dimensional quantum many-body systems with inverse-square interactions
• A new scalar product for nonsymmetric Jack polynomials
• Unified Fock space representation of fractional quantum Hall states
• Paths and partitions: combinatorial descriptions of the parafermionic states
• $\mathcal{P}\mathcal{T}$ deformation of Calogero-Sutherland models
• Creation operators for the Macdonald and Jack polynomials
• Time-dependent Dunkl-Pauli Oscillator
• Heisenberg Honeycombs Solve Veneziano Puzzle
• Intertwining Operators for a Degenerate Double Affine Hecke Algebra and Multivariable Orthogonal Polynomials
• Dunkl-Klein-Gordon Equation in Higher Dimensions
• Truncated Calogero-Sutherland Models on a Circle
• Bounding the Wigner Deformation Parameter in Harmonically Trapped Bose Gases
• Algebraic study on the $A_{N-1}$- and $B_N$-Calogero models with bosonic, fermionic and distinguishable particles
• Braid Structure and Raising-Lowering Operator Formalism in Sutherland Model
• The Dyson and Coulomb games
• Sutherland Models for Complex Reflection Groups
• Embedding Theorems for the Dunkl Harmonic Oscillator on the Line
• On the Schur expansion of Jack polynomials
• Mixed norm estimates for the Cesàro means associated with Dunkl--Hermite expansions
• Free boson realization of the Dunkl intertwining operator in one dimension
• The $B_2$ Harmonic Oscillator with Reflections and Superintegrability
• Orthogonality Measure on the Torus for Vector-Valued Jack Polynomials
• From Jack to Double Jack Polynomials via the Supersymmetric Bridge
• Application of the method of Bonan-Clark to the generalized Hermite polynomials
• Vector-valued Jack Polynomials and Wavefunctions on the Torus
• Symmetric functions in superspace: a compendium of results and open problems (including a SageMath worksheet)
• Spectral and Thermal Analysis of the Morse Potential within the Dunkl Formalism: Analytical Approximations and Applications
• Inversion Formulas for the Dunkl Intertwining Operator and Its Dual on Spaces of Functions and Distributions
• Rodrigues formulas for the Macdonald polynomials
• The quantum harmonic oscillator with icosahedral symmetry and some explicit wavefunctions
• W Algebras from AdS/CFT Correspondence
• On the differential equations of frozen Calogero-Moser-Sutherland particle models
• Hypoelliptic Dunkl equations in the space of distributions on $R^d$
• Symmetric functions in superspace
• Semilinear equations associated with Dunkl Laplacian
• A Superpolynomial Version of Nonsymmetric Jack Polynomials
• On the Generalized Ornstein-Uhlenbeck Semigroup
• Algebraic integrability of $\mathcal{P}\mathcal{T}$-deformed Calogero models
• Equivalence of the super Lax and local Dunkl operators for Calogero-like models
• Jack on a Devil's staircase
• Positivity of Dunkl's intertwining operator
• The N=2 supersymmetric Calogero-Sutherland model and its eigenfunctions
• Singular Vector of Ding-Iohara-Miki Algebra and Hall-Littlewood Limit of 5D AGT Conjecture
• On The Dunkl Intertwining Opereator
• Calogero-like model without rearrangement symmetry
• Absolute continuity of the measures of the Dunkl intetwining operator and its dualand applications
• An Integral Expression for the Dunkl Kernel in the Dihedral Setting
• A short proof of the integrality of the Macdonald (q,t)-Kostka coefficients