Quantum-mechanical treatment of two particles in a potential box

Abstract

In classical physics, there is a basic principle, namely "A particle cannot be located at the position of another one on the same time". Which consequences can be derived if this principle is transferred into quantum physics? For doing that, two distinguishable particles are considered to be trapped in a potential box by means of the Schr\"odinger equation. In result, the particles can necessarily be located only at discrete positions.