Degeneracy in Ring Hamiltonian

Classical Mechanics Level pending

A particle constrained to move on a ring can be described by one parameter, the angle \(\phi\) on the ring with respect to some coordinates. In quantum mechanics, an otherwise free particle constrained to move on this ring has the Hamiltonian

\[\hat{H} = -\frac{d^2}{d\phi^2}.\]

Which of the following correctly describes the spectrum of this Hamiltonian?

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