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