Mathematical Methods in the Physical Sciences · Problem 5.25

FUNCTIONS OF A COMPLEX VARIABLE — Mary Boas

Mathematics — Methods · parseval-theorem-normalization

Problem

Normalize

f(x)

in Problem 4.21; that is, find the factor

N

so that

\int_{-\infty}^{\infty} |Nf(x)|^2 = 1

. Let

\psi(x) = Nf(x)

, and find

\phi(p)

as given in Problem 24. Verify Parseval's theorem, that is, show that

\int_{-\infty}^{\infty} |\phi(p)|^2\, dp = 1