# Wave kernel for the Schrodinger operator with a Liouville potential

## TL;DR

This paper derives an explicit wave kernel formula for the Schrödinger operator with a Liouville potential, enabling applications to the telegraph equation and wave equations on hyperbolic spaces.

## Contribution

It provides a novel explicit formula for the wave kernel of the Schrödinger operator with Liouville potential, linking it to hyperbolic geometry and related equations.

## Key findings

- Explicit wave kernel formula for Schrödinger operator with Liouville potential
- Applications to telegraph and hyperbolic wave equations
- Enhanced understanding of wave propagation in hyperbolic spaces

## Abstract

In this note we give an explicit formula for the wave equation associated to the Schrodinger operator with a Liouville Potential with applications to the telegraph equation as well as the wave equation on the hyperbolic plane