An integral representation for the resolvent kernel with magnetic fields on the hyperbolic plane and applications to time dependent Schr\"odinger equations

TL;DR

This paper derives an integral representation for the resolvent kernel with a uniform magnetic field on the hyperbolic plane and applies it to explicitly solve time-dependent Schrödinger equations in this setting.

Contribution

It introduces a novel integral representation for the resolvent kernel under magnetic fields on the hyperbolic plane, enabling explicit solutions to related Schrödinger equations.

Findings

Derived an explicit integral formula for the resolvent kernel

Solved time-dependent Schrödinger equations explicitly

Provided tools for quantum mechanics on hyperbolic geometry

Abstract

In this paper we give an integral representation for the resolvent kernels with uniform magnetic field on the hyperbolic plane, as applications of our results we solve explicitly two times dependent Schr\"odinger equations with uniform magnetic field on the hyperbolic plane