Some exact solutions of the Schr\"odinger--Poisson system in spaces of constant sectional curvature

TL;DR

This paper derives exact stationary solutions for the Schr"odinger--Poisson system on curved spaces with constant curvature, providing insights into quantum systems influenced by geometry.

Contribution

It presents new closed-form solutions of the Schr"odinger--Poisson system on manifolds of constant curvature, extending previous work to curved geometries.

Findings

Closed-form stationary solutions for specific dimensions.

Examples of solutions with nonzero background.

Insights into quantum systems on curved spaces.

Abstract

We consider the Schr\"odinger--Poisson system on the complete, simply-connected Riemannian manifolds of constant sectional curvature. We obtain closed-form stationary spherically-symmetric solutions for the homogeneous equations for certain dimensions, and give some basic examples of solutions with a nonzero background.