An electron is moving freely inside a one-dimensional infinite potential box with walls at x=0 and x=a. If the electron is initially in the ground state (n=1) of the box and if we suddenly quadruple the size of the box (i.e., the right-hand side wall is moved instantaneously from x=a to x=4a), calculate the probability of finding the electron in:
(a) the ground state of the new box and
(b) the first excited state of the new box.