# New integrable two-centre problem on sphere in Dirac magnetic field

## TL;DR

This paper introduces a new integrable two-centre problem on a sphere influenced by a Dirac magnetic monopole, featuring unique algebraic potentials and quadratic integrals in both classical and quantum contexts.

## Contribution

It presents a novel family of integrable systems on a sphere with a magnetic monopole, expanding the class of known integrable models with special algebraic potentials.

## Key findings

- New integrable two-centre systems on a sphere with magnetic monopole
- Presence of algebraic potential and quadratic integral in classical and quantum forms
- Extension of integrable models in magnetic field contexts

## Abstract

We present a new family of integrable versions of the Euler two-centre problem on two-dimensional sphere in the presence of the Dirac magnetic monopole of arbitrary charge. The new systems have very special algebraic potential and additional integral quadratic in momenta, both in classical and quantum versions.