 Quantum rotor

A quantum coordinate on a circle with kinetic Hamiltonian ${\ell }^2/(2I)$. Periodic wavefunctions have angular momentum $\hslash n$ and energy ${\hslash }^2{n}^2/(2I)$ for integer $n$. Its thermal trace has both a momentum-eigenstate sum and a topological winding-path representation. Twisted boundary conditions or flux would modify this spectrum and are separate models.