1. An electron in a 1-D box with length, a, has a wave function: 4(x) = N * (Cx - x2). The potential inside of the box is V(0 S x S a) = 0, and the potential outside the box is infinite. a) 5pts. Find a value for C that satisfies the boundary conditions (0) = 0 and 4(a) = 0 b) 15pts. Find a value for the constant / that normalizes the wavefunction. c) 5pts. What is the probability of finding the electron inside of the box? d) 15pts. What is the probability of finding the electron between x = 0 and x = a/2 ? e) 10pts. Is the wavefunction an eigenfunction of the Hamiltonian operator