Bound States

Again, using the results for Part 1, and also (9.06), (9.07), and (9.19), we see that

Then substituting in (9.17) by means of (9.19) and (9.20) we arrive at

compare (9.18). Key inequalities are

Substituting these results in the bound

for ^Y,,(l-d,xO(H), we find that this variation is O(U-~) , O ( ~ - ~ l n u ) , or o(u-~/"), according as a < 1, a = 1, or a > 1.