Imagine a bead of mass m that slides frictionless around a circular wire ring of circumference L. (This is just like a free particle, except that ψ(x + L) = ψ(x).) Find the stationary states (with appropriate normalization) and the corresponding allowed energies. Note that there are two independent solutions for each energy E„—corresponding to clockwise and counter-clockwise circulation; call them if£(x) and How do you account for this degeneracy, in view of the theorem in Problem 2.45 (why does the theorem fail, in this case)?
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