Quantum exotic: A repulsive and bottomless confining potential

الأصل · EN

On a simple model V(x,y)=Ax²+By²+Cx²y²+D(x²y⁴+x⁴y²) we demonstrate that even in a classically repulsive regime (i.e., at couplings which make the potential decreasing to -∞ 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.