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[tex] \Phi(p, 0) = \frac{1}{\sqrt{2 \pi \hbar}}\int_{-\infty}^\infty e^{-i p x/\hbar} \frac{A}{x^2+a^2}dx.[/tex]

The problem implies an exact solution can be found since it subsequantly asks you to check normalization and compute the expected values of p and p

^{2}using the transformed fn. Mathematica evaluates the transform in terms of a special fn MeijerG.