Resolvent kernels and time dependent Schr\" odinger equations under magnetic field on the hyperbolic half plane $\H$ and the Morse potential on the real line $\

TL;DR

This paper derives exact formulas for resolvent kernels and solutions of time-dependent Schrödinger equations in two settings: hyperbolic half plane with magnetic field and Morse potential on the real line, advancing mathematical physics understanding.

Contribution

It provides explicit formulas for resolvent kernels and solutions in these two specific quantum mechanical models, which were previously not fully characterized.

Findings

Exact resolvent kernels derived for hyperbolic half plane with magnetic field

Explicit solutions obtained for Schrödinger equations with Morse potential

Enhances mathematical tools for quantum systems on curved spaces and with potentials

Abstract

This paper deals with exact formulas for the resolvent kernels and exact solutions of time dependent Schr\"odinger equations under a uniform magnetic field on the hyperbolic half plane $\H$, and under a diatomic molecular Morse potential on the real line $\R$.