In the usual statement of the Particle in a Box problem, we assume two infinite potential barriers, to hold its wavefunction constrained, so it goes to zero on both ends:
But instead of invoking some unphysical infinite barrier, could be the case the wave just return to the same point. Using a simple warp drive(two paperclips):
That was for the X coordinate. So our one-dimensional box became a ring. Doing the same with the Y coordinate would get us a torus. With Z we would get a torus in the fourth dimension, and our box would be a single particle, inhabiting a boundless tiny universe.
So, our particle in a box is the actually a particle in a hypertorus?
At first I posted this question in the recently created materials modeling stackexchange, but it wasn't well received, quickly getting -6 votes and being deemed offtopic and deleted. People there pointed the physics stackexchange as a more adequate forum, so I'm giving it a try here.