A particle of mass m is fixed at one end of a rigid rod of negligible mass and length R. The other end of the rod rotates in the xy plane about a bearing located at the origin, whose axis is in the z-direction.
(a) Write the system's total energy in terms of its angular momentum L.
(b) Write down the time-independent Schrödinger equation of the system. Hint: In spherical coordinates, only φ varies.
(c) Solve for the possible energy levels of the system, in terms of m and the moment of inertia I=mR2.
(d) Explain why there is no zero-point energy.