Problem 3 (20 points) A particle in three-dimensions is in a state described by the following wavefunc- tion: (r) = N where r = Irl. 1. Determine the constant /V such that w(r) is normalized 2. Determine the probability that the modulus k of the wave vector of the particle has a value between 0 and ar. 3. Check that the probability for k to assume all possible values is indeed 1