Revise your solution to Prob. 8.60 to treat the one-dimensional harmonic oscillator using particle-in-a-box (pib) basis functions. Recall that in Section 4.4 we found that for Er ( 5, the wave function can be taken as zero outside the region -5 ( xr ( 5, where Er and xr are defined by (4.75) and (4.76). Therefore, we shall take the pib basis functions to extend from -5 to 5, with the center of the "box" at xr = 0. Since the box has a length of 10 units in xr, we have (j = (2/10)1/2 sin[j((xr + 5)/10] for ( xr ( ( 5 and (j = 0 elsewhere. You will also need to revise the kinetic- and potential-energy matrix elements. Increase the number of pib basis functions until all energy values with Er < 5 are accurate to three decimal places. Check the appearance of the lowest three variation functions. Which pib basis functions contribute most to the ground state? to the first excited state?