Remember that the eigenvectors are a complete basis. That is, any wavefunction can be decomposed as a linear combination of eigenvectors n. Consider a potential V (x) = 0 for 0 < x < L and infinite otherwise. (a) Find the eigenvectors of the system [5 pts] (b) What would the wavefunction look like if we had equal probability of finding the electron everywhere inside the box? [5 pts] (c) Decompose as a linear combination of the particle in a box eigenvectors. That is, find the coefficients cn such that P n Cn n [5 pts] (d) Plot the approximation to PN n=0 Cn nfor N=10 and N=20 when L=1 nm [10 pts] 2