Quantum exotic: A repulsive and bottomless confining potential

TL;DR

This paper investigates a quantum model with a complex potential that, despite being classically repulsive and unbounded below in some directions, can still support discrete bound states due to quantum effects, revealing a stability boundary.

Contribution

It introduces a specific multi-parameter potential model demonstrating quantum stability in classically repulsive regimes and identifies a critical boundary for particle escape.

Findings

Quantum bound states exist even in classically repulsive potentials.

A critical boundary separates stable bound states from particle escape.

Potential parameters determine the stability and escape behavior.

Abstract

On a simple model $V(x,y)=A\,x^2+B\,y^2+C\,x^2y^2+D\,(x^2y^4+x^4y^2)$ we demonstrate that even in a classically repulsive regime (i.e., at couplings which make the potential decreasing to $-\infty$ in some directions) quantum mechanics may still support the purely discrete spectrum of bound states. In our example, there exists a critical boundary of this domain of stability where a further increase of repulsion causes an explosive escape of particles in infinity.