Bell shaped gaussian function

The bell-shaped Gaussian function, m) = sap H (\"'3'\")2], is one of the most widely used functions in science and technology. The parameters or and s 1) 0 are prescribed real numbers. Make a program for evaluating this function when m = D, a = 2, and a: = 1. Verify the program's rllult by comparing with hand calculations on a calculator. Show that the inverse Fourier transform of a Gaussian function in k-space F(k) = V2mode *"is another Gaussian function in position space f(x) = Ae *(20") (Hint: the integration technique you need to use here is similar to that given in class for the Fourier transform from /(x) to F(k).)1 The Dirac o function The delta function can also be described by a Gaussian function 6(x) = lim da (@) = lim exp 0-0 0-0 aV 2TT 2a Use the definition of the o function Eq.(1) to prove the following identities. S(x - xo)f(x) dx = f(x0) - DO Please use Gaussian .OO function to calculate ! 8' (x) f (2) = -f'(2) - Do