Open AccessRational extension of many particle systems
Author(s) -
Bhabani Prasad Mandal
Publication year - 2022
Publication title -
acta polytechnica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.207
H-Index - 15
eISSN - 1805-2363
pISSN - 1210-2709
DOI - 10.14311/ap.2022.62.0090
Subject(s) - isospectral , extension (predicate logic) , eigenfunction , bound state , quantum , harmonic oscillator , physics , construct (python library) , pure mathematics , mathematics , theoretical physics , quantum mechanics , computer science , eigenvalues and eigenvectors , programming language
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.