Quasi-Exactly-Solvable Many-Body Problems

TL;DR

This paper presents explicit examples of quasi-exactly-solvable many-body problems on the line, related to the hidden algebra sl_N, with some having infinitely many known eigenstates and others only a finite number, both degenerating to the Calogero model.

Contribution

It introduces new classes of quasi-exactly-solvable N-body problems related to sl_N algebra, expanding the set of solvable models in many-body quantum mechanics.

Findings

Examples of quasi-exactly-solvable N-body problems are provided.

Some models have infinitely many known eigenstates, others only a finite number.

Both types degenerate to the Calogero model.

Abstract

Explicit examples of quasi-exactly-solvable $N$-body problems on the line are presented. These are related to the hidden algebra $sl_N$, and they are of two types -- containing up to $N$ (infinitely-many eigenstates are known, but not all) and up to 6 body interactions only (a finite number of eigenstates is known). Both types degenerate to the Calogero model.