(a). What are the energies and energy eigenfunctions for a non-relativistic particle of mass m moving on a ring of radius Ras shown in Fig. (a)?(b). What are the energies and eigenfunctions if the ring is doubled (each loop still has radius R) shown in Fig. (b)?(c) If the particle has a charge q. What are the energies and energy eigenfunctions if a very long solenoid containing amagnetic flux passes the rings, as shown in Fig. (c)? Assume the system does not radiate electromagnetically.Fig. (a)Fig. (b)Fig. (c)

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(a). What are the energies and energy eigenfunctions for a non-relativistic particle of mass m moving on a ring of radius R as shown in Fig. (a)?