Some Exactly Solvable Three-Body Problems in One dimension
Avinash Khare (Institute of Physics, Bhubaneswar, India), and Rajat K., Bhaduri (Dept.of Physics, Astronomy, Mcmaster Univ., Canada)
TL;DR
This paper extends the class of exactly solvable one-dimensional three-body problems by leveraging supersymmetric quantum mechanics, providing explicit solutions for spectra and eigenfunctions with various potentials.
Contribution
It introduces new solvable three-body potentials in one dimension using supersymmetric quantum mechanics, expanding the set of algebraically solvable models.
Findings
Explicit eigenspectra and eigenfunctions for new potentials
Solutions applicable with and without confinement
Enhanced understanding of solvable quantum many-body systems
Abstract
The three-body problem in one-dimension with a repulsive inverse square potential between every pair was solved by Calogero. Here, the known results of supersymmetric quantum mechanics are used to propose a number of new three-body potentials which can be solved algebraically. Analytic expressions for the eigenspectrum and the eigenfunctions are given with and without confinement.
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