I need detailed answers for part C and D. Please show me detailed steps.

2. The quantum states of a particle moving freely in a circle of radius r are described by ' 1%(6) = Gem\" where C' is a constant, 9 denotes angle, as = 0, i1,j:2, . .. is an integer identifying the quantum state of the particle, and can is constant for a given n. a) Show that 1%(9) satises b) Find can such that c) Find the value of C such that 211' WW = 1 0 (1) Show that any two $46) and m(9) with m 75 n satisfy 211' 0 pmwmww = 0