a) Damping by friction often leads to exponentially-decaying functions, such as
f(x)=exp(-a|x|),a>0
. Show that the Fourier transform,
g(k)=(1)/(2\pi )\int e^(ikx)f(x)dx
, of this function is a Lorentzian, i.e.
∼(1)/(a^(2)+k^(2))
.

Question

a) Damping by friction often leads to exponentially-decaying functions, such as

f(x)=exp(-a|x|),a>0

. Show that the Fourier transform,

g(k)=(1)/(2\pi )\int e^(ikx)f(x)dx

, of this function is a Lorentzian, i.e.

∼(1)/(a^(2)+k^(2))

.

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(Solved): a) Damping by friction often leads to exponentially-decaying functions, such as f(x)=exp(-a|x|),a> ...