# Quantum support to BoHua Sun's conjecture

## TL;DR

This paper explores the application of BoHua Sun's generalized Kepler's third law to quantum systems of self-gravitating particles, suggesting a potential bridge between classical orbital laws and quantum mechanics.

## Contribution

It demonstrates that Sun's conjecture can be extended to quantum N-body systems with appropriate period selection, broadening its scope beyond classical mechanics.

## Key findings

- Sun's law applies to quantum self-gravitating systems with suitable period choices
- The generalized Kepler's third law can describe quantum N-body dynamics
- Potential link between classical orbital laws and quantum gravitational systems

## Abstract

A generalization of the Kepler's third law has been proposed by BoHua Sun for $N$-body periodic orbits in a Newtonian gravitation field. In this paper, it is shown that this formula can apply for a quantum system of $N$ self-gravitating identical particles, for a good choice of the period for the quantum motion.