Answers for Assigned Problems

4.13 (a) <r> = 3a/2
              <r²> = 3 a²

        (b) <x> = 0
              <x²> = a²

        (c) <x²> = 12 a²

4.14.  r = a

4.16 (a) E_n(Z) = Z²E_n
              a(Z) = a/Z
              R(Z) = Z²R
              For Z=2, l ranges from 2.28 x 10 ^-8 m to 3.04 x 10 ^-8 m in the ultraviolet.
              For Z=3, l ranges from 1.01 x 10 ^-8 m to 1.35 x 10 ^-8 m in the ultraviolet.

4.18 Answer in problem.

4.20 Proof.

4.22 (a) 0.
        (b) Y_k^k = A (e^if sin q)^k
        (c) A = [1/(2^k+1 k!)] sqrt [(2k+1)!/p].

Last revised 2005/04/18