A class of exactly solvable rationally extended Calogero–Wolfes type 3-body problems

Kumari, Niraj; Yadav, Rajesh K.; Khare, Avinash; Mandal, Bhabani Prasad

doi:10.1016/j.aop.2017.07.022

Cited by 12 publications

(3 citation statements)

References 54 publications

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“…Rational extensions have also been carried out for non-Hermitian systems [6,19,[29][30][31][32]. Even though most of the rational extensions are for the one dimensional and/or one particle exactly solvable systems, the research in this field has also been extended to many particle systems [24,25,27]. We have done several works on rational extensions for many particle systems.…”

Section: Introductionmentioning

confidence: 99%

Rational extension of many particle systems

Mandal

2022

Acta Polytech

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In this talk, we briefly review the rational extension of many particle systems, and is based on a couple of our recent works. In the first model, the rational extension of the truncated Calogero-Sutherland (TCS) model is discussed analytically. The spectrum is isospectral to the original system and the eigenfunctions are completely expressed in terms of exceptional orthogonal polynomials (EOPs). In the second model, we discuss the rational extension of a quasi exactly solvable (QES) N-particle Calogero model with harmonic confining interaction. New long-range interaction to the rational Calogero model is included to construct this QES many particle system using the technique of supersymmetric quantum mechanics (SUSYQM). Under a specific condition, infinite number of bound states are obtained for this system, and corresponding bound state wave functions are written in terms of EOPs.

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Section: Introductionmentioning

confidence: 99%

Rational extension of many particle systems

Mandal

2022

Acta Polytech

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“…those where the potential is of the form 'oscillator/inverse square') have received considerable attention, and many interesting properties have been discovered [14][15][16][17][18][19][20][21][22][23][24][25][26]. There are also many works which have attempted to obtain new ES models by extending existing ones through separation of variables [27][28][29].…”

Section: Introductionmentioning

confidence: 99%

Extended Calogero models: a construction for exactly solvable kN-body systems

Chen

Links

Marquette

et al. 2018

J. Phys. A: Math. Theor.

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“…those where the potential is of the form "oscillator/inverse square") have received considerable attention, and many interesting properties have been discovered [53][54][55][56][57][58][59][60][61][62][63][64][65]. There are also many works which have attempted to obtain new ES models by extending existing ones through separation of variables [66][67][68]. More complicated extensions, which have connections with orthogonal polynomials, can be obtained by PT (parity and time reversal) symmetric quantum mechanics [69][70][71].…”

Section: Introductionmentioning

confidence: 99%

New families of exactly solvable many-body models and superintegrable systems

Chen¹

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In this thesis, we study various extensions of Calogero models and superintegrable systems. We construct a kN-body one-dimensional model which reduces to the familiar Calogero model when k = 1. We present a class of many-body systems that are equivalent to harmonic oscillators. We study interesting extensions of the D-dimensional Coulomb-Kepler system and show that when the extension satisfies certain conditions, then some components of the Laplace-Runge-Lenz vector can be extended to conserved quantity of the new models. By introducing block separation of variables, we construct the Kepler-singular oscillator type models which are a new family of superintegrable systems. We also use separation of variables to obtain the energy spectrum, eigenfunctions and corresponding quadratic algebraic structures. Separation of variables is not only used for solving eigenvalue problems but also provides us with new tools for generalizing superintegrable systems. We generalize the double harmonic-singular oscillators and Kepler-singular oscillator systems. The integrals of new models now can involve angles from block spherical coordinates. A derivation of more general quadratic algebraic structures is presented as well. We also give examples to show they can be solved in terms of so-called X 1 Jacobi polynomials. ABSTRACT iii Declaration by authorThis thesis is composed of my original work, and contains no material previously published or written by another person except where due reference has been made in the text. I have clearly stated the contribution by others to jointly-authored works that I have included in my thesis.

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A class of exactly solvable rationally extended Calogero–Wolfes type 3-body problems

Cited by 12 publications

References 54 publications

Rational extension of many particle systems

Rational extension of many particle systems

Extended Calogero models: a construction for exactly solvable kN-body systems

New families of exactly solvable many-body models and superintegrable systems

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