Explicit formulas for the eigenfunctions of the N-body Calogero model

Abstract

We consider the quantum Calogero model, which describes N non-distinguishable quantum particles on the real line confined by a harmonic oscillator potential and interacting via two-body interactions proportional to the inverse square of the inter-particle distance. We elaborate a novel solution algorithm which allows us to obtain fully explicit formulas for its eigenfunctions, for arbitrary coupling parameter and particle number. We also show that our method applies, with minor changes, to all Calogero models associated with classical root systems.

References in corpus (6)

• A multispecies Calogero model
• Q-operator and factorised separation chain for Jack polynomials
• Algorithms to solve the Sutherland model
• Remarkable identities related to the (quantum) elliptic Calogero-Sutherland model
• Explicit formulas for the generalized Hermite polynomials in superspace
• A method to derive explicit formulas for an elliptic generalization of the Jack polynomials

Cited by in corpus (4)

• A unified construction of generalised classical polynomials associated with operators of Calogero-Sutherland type
• Singular Eigenfunctions of Calogero-Sutherland Type Systems and How to Transform Them into Regular Ones
• An Explicit Formula for Symmetric Polynomials Related to the Eigenfunctions of Calogero-Sutherland Models
• Closed-form propagator of the Calogero model