Rationally extended many-body truncated Calogero-Sutherland model

Abstract

We construct a rational extension of the truncated Calogero-Sutherland model by Pittman et al. The exact solution of this rationally extended model is obtained analytically and it is shown that while the energy eigenvalues remain unchanged, however the eigenfunctions are completely different and written in terms of exceptional X1 Laguerre orthogonal polynomials. The rational model is further extended to a more general, the Xm case by introducing m dependent interaction term. As expected, in the special case of m = 0, the extended model reduces to the conventional model of Pittman et al. In the two appropriate limits, we thereby obtain rational extensions of the celebrated Calogero-Sutherland as well as Jain-Khare models.

arXiv comment09 pages, LaTex, No fig

References in corpus (29)

• An extended class of orthogonal polynomials defined by a Sturm-Liouville problem
• Exceptional orthogonal polynomials, exactly solvable potentials and supersymmetry
• Rational extensions of the quantum harmonic oscillator and exceptional Hermite polynomials
• Exactly Solvable Quantum Mechanics and Infinite Families of Multi-indexed Orthogonal Polynomials
• Another set of infinitely many exceptional (X_{\ell}) Laguerre polynomials
• Two-step Darboux transformations and exceptional Laguerre polynomials
• Isospectrality of conventional and new extended potentials, second-order supersymmetry and role of PT symmetry
• Solvable rational extensions of the isotonic oscillator
• Exceptional orthogonal polynomials and the Darboux transformation
• Exceptional orthogonal polynomials and exactly solvable potentials in position dependent mass Schroedinger Hamiltonians
• Asymptotic behaviour of zeros of exceptional Jacobi and Laguerre polynomials
• An exactly solvable many-body problem in one dimension
• A class of N-body problems with nearest- and next-to-nearest neighbour interactions
• Rationally-extended radial oscillators and Laguerre exceptional orthogonal polynomials in kth-order SUSYQM
• The Scattering amplitude for Newly found exactly solvable Potential
• Parametric symmetries in exactly solvable real and P T symmetric complex potentials
• Effect of Position-dependent Mass on Dynamical Breaking of Type B and Type X_2 N-fold Supersymmetry
• Group theoretic approach to rationally extended shape invariant potentials
• Scattering Amplitudes for Multi-indexed Extensions of Solvable Potentials
• Truncated Calogero-Sutherland models
• A class of exactly solvable rationally extended non-central potentials in Two and Three Dimensions
• Scattering amplitudes for the rationally extended P T symmetric complex potentials
• Shape invariance and equivalence relations for pseudowronskians of Laguerre and Jacobi polynomials
• Quasi exactly solvable extension of Calogero model associated with exceptional orthogonal polynomials
• A class of exactly solvable rationally extended Calogero-Wolfes type 3-body problems
• A short note on "Group theoretic approach to rationally extended shape invariant potentials" [Annals of Physics 359, 46 (2015)]
• The quantum n-body problem in dimension $d\ge n-1$: ground state
• Coherent states for ladder operators of general order related to exceptional orthogonal polynomials
• Quartic anharmonic many-body oscillator

Cited by in corpus (3)

• Supersymmetry and Shape Invariance of exceptional orthogonal polynomials
• Solutions of (1+1)-dimensional Dirac equation associated with exceptional orthogonal polynomials and the parametric symmetry
• Taxonomy of integrable and ground-state solvable models: Jastrow wave functions on graphs and parent Hamiltonians