Fractional Schr\"odinger equations with singular potentials of higher order. II: Hypoelliptic case

TL;DR

This paper extends the analysis of fractional Schr"odinger equations with singular potentials to hypoelliptic operators on graded Lie groups, broadening the understanding of such equations in more general geometric contexts.

Contribution

It introduces a framework for studying fractional Schr"odinger equations with singular potentials in the hypoelliptic setting on graded Lie groups, extending previous Euclidean results.

Findings

Analysis of hypoelliptic fractional Schr"odinger equations with singular potentials

Extension of classical results to graded Lie group setting

Framework for future research in hypoelliptic quantum mechanics

Abstract

In this paper we consider the space-fractional Schr\"odinger equation with a singular potential for a wide class of fractional hypoelliptic operators. Such analysis can be conveniently realised in the setting of graded Lie groups. The paper is a continuation and extension of a previous one where the classical Schr\"odinger equation on $\mathbb R^n$ with singular potentials was considered.