(a) Expand the function ((x) = -1 for 0 ( x ( l and ((x) =...

(a) Expand the function ((x) = -1 for 0 ( x ( ½ l and ((x) = 1 for 1/2 l < x ( l in terms of the particle-in-a-box wave functions. (Since ( is discontinuous at ½ l, the expansion cannot be expected to represent ( at this point. Since ( does not obey the particle-in-a-box boundary conditions of being zero at x = 0 and x = l, the expansion will not represent ( at these points. The expansion will represent ( at other points.) (b) Calculate the percent error at x = l/4 when the first 1, 3, 5, and 7 nonzero terms are taken in this expansion.