A quantum particle constrained to a circle has integer angular-momentum eigenvalues and periodic position eigenfunctions. Its propagator can be written either as a sum over angular momenta or as a sum over winding number sectors.
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A "particle in a ring" is a fundamental problem in quantum mechanics that describes a quantum particle constrained to move on the circumference of a circle (or ring) of a fixed radius. This model is significant for understanding certain concepts in quantum mechanics, such as quantization, angular momentum, and the behavior of particles in systems with circular symmetry.