2. The quantum states of a particle moving freely in a circle of radius r are described by was!) = 06\"\" where C is a constant, 9 denotes angle, n = 0,:L-1, i2, . . . is an integer identifying the quantum state of the particle, and w\" is constant for a given n. a) Show that $.10?) satises (Fwy. (62 = with\" b) Find mu such that 11":(9 + 21'1") = 145:.(9) c) Find the value of C such that in f IwnIIHJIZdB = 1 o (1) Show that any two #5,,(6) and wmw) with m, y! n satisfy '21!' f0 ;(9)1bm(9)d9 = o