A Simple Volcano Potential with an Analytic, Zero-Energy, Ground State

TL;DR

This paper introduces a simple, analytically solvable volcano potential with a zero-energy ground state, useful for modeling higher-dimensional gravity scenarios and understanding KK modes.

Contribution

It presents a new supersymmetric volcano potential with an exact zero-energy ground state and analytically solvable KK modes, aiding theoretical physics research.

Findings

Potential is supersymmetric with an analytic zero-energy ground state.

KK modes are analytically solvable within this potential.

Special cases clarify the physics of higher-dimensional gravity.

Abstract

We describe a simple volcano potential, which is supersymmetric and has an analytic, zero-energy, ground state. (The KK modes are also analytic.) It is an interior harmonic oscillator potential properly matched to an exterior angular momentum-like tail. Special cases are given to elucidate the physics, which may be intuitively useful in studies of higher-dimensional gravity.