Integrability, intertwiners and non-linear algebras in Calogero models

TL;DR

This paper explicitly constructs conserved charges and their nonlinear algebras for specific Calogero models, revealing additional charges at integral couplings and providing explicit wave functions.

Contribution

It introduces explicit conserved charges and nonlinear algebra structures for certain Calogero models, including extra charges at integral couplings.

Findings

Complete sets of conserved charges are presented.

Nonlinear algebra structures are derived.

Explicit low-level wave functions are tabulated.

Abstract

For the rational quantum Calogero systems of type $A_1{\oplus}A_2$, $AD_3$ and $BC_3$, we explicitly present complete sets of independent conserved charges and their nonlinear algebras. Using intertwining (or shift) operators, we include the extra `odd' charges appearing for integral couplings. Formulae for the energy eigenstates are used to tabulate the low-level wave functions.