Open AccessThe exact solution of a three-body problem of Calogero type in one dimension by the SUSY-QM and SGA methods
Author(s) -
I. Sekhane
Publication year - 2021
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/1766/1/012027
Subject(s) - supersymmetry , hamiltonian (control theory) , equivalence (formal languages) , eigenvalues and eigenvectors , algebraic number , nonlinear system , type (biology) , lie algebra , algebra over a field , mathematics , dimension (graph theory) , physics , mathematical physics , pure mathematics , quantum mechanics , mathematical analysis , mathematical optimization , ecology , biology
Analytic expressions of the eigenvalues for a non-relativistic Hamiltonian of a three-body problem of the Calogero type can be derived using both the well known method of supersymmetric quantum mechanics SUSY-QM and an independent group theoretic method, namely the spectrum generating algebra SGA. We demonstrate the equivalence of the two methods by developing an algebraic framework through the shape invariance SI property with a change of parameters which involves nonlinear extensions of Lie Algebra.