Unbound States in an Almost Infinite Deep Potential.

The behavior of a quantum particle in an almost infinite deep potential is investigated. By means of analytical and numerical methods, it is demonstrated that even if the potential is infinitely deep, the particle's eigenstate can still be unbound, which contradicts the previous belief that an infinite deep potential can only sustain bound states. These findings shed new light on the eigenstate problem of quantum mechanics. [ABSTRACT FROM AUTHOR]