A particle has a Hamiltonian of the following form Н ħ² 2² 1 ə + + 1 8² 8² + r² Ə6² əz² + V (r, o, z), 2m Ər² rər where (r, o, z) are cylindrical coordinates. (a) Describe what is meant by an observable quantity A is a constant of motion in quantum mechanics and the condition required for Â. (b) What symmetry property must be satisfied by the potential energy field V(r, o, z) so that the z-component of the momentum, an observable described by the operator Pz = -ih- Ə Əz is a constant of the motion? (c) Then what symmetry property must be satisfied by the potential energy field V so that the z-component of the orbital angular momentum described by the operator L₂=-ih- Ə до is also a constant of the motion?