String, ring, sphere: visualizing wavefunctions on different topologies

A quantum system´s state is described by a complex wave function, which can be supported on different topologies - for example, one-dimensional open space, a closed one-dimensional ring, or a two-dimensional surface of a sphere. Interactive tools represent the quantum state of a single particle constrained to different topologies, while stressing the underlying superposition principle, which is independent of topology. The insight gained by visualizing the same phenomena in different geometrical contexts contributes to the students´ ability to abstract, which is the key to understanding quantum phenomena in more complex systems.