Evaluate the z-component of the angular momentum and the kinetic energy of a particle on a ring

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Evaluate the z-component of the angular momentum and the kinetic energy of a particle on a ring that is described by the (unnormalized) wavefunctions (a) e, (b) e−2iφ, (c) cos φ, and (d) (cos χ)e+(sin χ)e−iφ.

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