3. A particle of mass 11 is xed at one end of a rigid rod of negligible mass and length R. The other end of the rod rotates in the x-y plane about a bearing located at the origin, whose axis is in the z direction. This two-dimensional "rigid rotator" is illustrated below. (a) Write an expression for the total energy of the system in terms of its angular momentum L. (Hint: Set the constant potential energy equal to zero, and then express the kinetic energy in terms of L.) (b) By introducing the appropriate operators into the energy equation, convert it into the Schroedinger equation hz azww) _ r MW) 2 u 2! 8m {Ft where I : uR2 is the rotational inertia, or moment of inertia, and 'thl is the wave function written in terms of the angular coordinate