1. The problem statement, all variables and given/known data Consider the one dimensional wave funciton give below. a) Draw a graph of the wave function for the region defined. b) Determine the value of the normalization constant c) what is the probability of finding the particle between x = 0 and x = a/2 d) show that the wave fucntion is a solution of the non-relativistic wave equation (Schrodinger equation) for the potential energy function give below. ψ(x) = A(a^2-x^2) for -a < x < +a ψ(x) = 0 for x< -a and x > a U(x) = -((h bar)^2/ma^2)(x^2/(a^2-x^2)) 2. Relevant equations shown above 3. The attempt at a solution a) b) a ∫ ψ(x)^2 dx =1 -a a ∫ (A(a^2-x^2))^2 dx = 1 -a A = (√15 )/4√a^5 c) 39.4% d) I was given the question without answer, some help verifying my answer would be appreciated!!