Quantum exotic: A repulsive and bottomless confining potential

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.