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Gaussian Integrals In our brief foray into quantum chemistry, we will need to evaluate a lot of gaussian integrals. These exercises will be a first step toward a working quantum chemistry program. Gaussian Functions A one-dimensional gaussian function has the form g(x) = e-a(z-A)? o is called the "exponent" and A is called the "center" of the function. Write a function that takes two arguments, an exponent and a center, and plots the gaussian function g().input System output if input : selta function Systeron - Sella function Theme out put also salta function i-e output : Sits * Sects = sits if input : Gaussian function Systeron : Gaussian function Then output also Gaussian function i've output = 2it x 2 Gaussian functions -Tit 21 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