Integrable time-dependent central potentials

TL;DR

This paper classifies and constructs new integrable time-dependent central potentials, extending previous results, and applies them to various physical systems including oscillators, Kepler potentials, and Yukawa interactions.

Contribution

It provides a complete classification of integrable time-dependent central potentials with specific first integrals, filling gaps in previous research.

Findings

Explicit forms of new integrable potentials are derived.

Applications include integrable oscillators and generalized Kepler problems.

Wavefunctions for a new class of potentials are obtained.

Abstract

The integrable time-dependent central potentials that admit linear and quadratic first integrals other than those constructed from the angular momentum are determined. It is shown explicitly that previous answers to this problem are incomplete. The results are applied in order to find the integrable time-dependent oscillators, the integrable time-dependent generalized Kepler potentials, a class of integrable binary systems with variable mass, and the integrable Yukawa and interatomic potentials with time-dependent parameters. Finally, a new class of integrable potentials is integrated and the corresponding wavefunction is determined.