Consider a free particle with v(2) = 0, e > 0 with mass m in a periodic box with length l: (x, t) = 4(1) f(t) = aeikr + be-ikret (1) (a) find k in terms of e and l. (b) the wave function and its derivative must be continuous. since the point x = 0 is identified with x = l, write down the rsulting conditions and calculate the allowed energy levels.