What is the Fourier transform of Using Plancherel's theorem, show that Co...

What is the Fourier transform of Using Plancherel's theorem, show that

Comment: This formula gives any respectable mathematician apoplexy. Although the integral is clearly infinite when x = 0, it doesn't converge (to zero or any-thing else) when since the integrand oscillates forever. There are ways to patch it up (for instance, you can integrate from -L to +L, and interpret Equation 2.144 to mean the average value of the finite integral, as The source of the problem is that the delta function doesn't meet the requirement (square-integrability) for Plancherel's theorem (see footnote 33). In spite of this, Equation 2.144 can be extremely useful, if handled with care.