Quantum bungee jumping

TL;DR

This paper introduces the concept of quantum bungee jumping, where a specially designed potential confines particles to the positive half-line despite diverging to negative infinity at zero, challenging classical intuition.

Contribution

It presents a novel quantum confinement mechanism using a potential that diverges negatively at zero, with analysis of its eigenstates and spectrum.

Findings

Potential can confine particles despite diverging to -∞ at zero

Particles exhibit a bouncing behavior instead of falling off a cliff

Eigenstates and spectrum are characterized for the specific potential

Abstract

We show how a potential that is well-defined everywhere on the positive half-line, but diverges to $-\infty$ as $x\rightarrow 0^+$, may still be able to dynamically confine a particle to the (positive) half-line. We shall call this effect quantum bungee jumping: in the familiar quantum tunneling scenario one heading towards a wall is expected to bounce off it but instead passes through, while in the present scenario one jumping off a cliff is expected to fall but instead is pulled back. We discuss a particular example of a potential displaying this property, and study its energy eigenstates and spectrum.