Physics 471 Problem Set 8 Fall 2006
31. Griffiths Problem A.9
32. Griffiths Problem A.23
33. Griffiths Problem A.25
34. Griffiths Problem A.28 Part (a)
35. An inner product for functions defined on 0 ≤x≤ ∞ can be defined as
hg|fi=Z∞
0
dx g∗(x)f(x)e−x.
(a) Show that hg|fiis a properly defined inner product, i.e. hg|fi∗=hf|gi,hf|fi ≥ 0.
(b) Since the functions f(x) in the space have a power series expansion, the monomials
xn, n = 0,1,2,· · · form a basis. Use the Gram-Schmidt method to construct the
first three members of an orthonormal basis of polynomials for this space. Hint: The
required integrals are all of the form
Z∞
0
dx xne−x=n!.
Note: The first four problems are easily attacked using readily available software, e.g. Math-
ematica. I encourage you to work through these problems using your own fund of knowledge
before checking the results with your favorite software package.