Derive an analytical formula for the upper-level population N2(t) in the simplified upper-level

laser model , assuming a Gaussian rather than a square time-varying

pump pulse Rp(t). Plot the peak inversion that is produced vs the parameter Tp/t2.

Hint: a very useful approximate formula for the error function erf(x), accurate to ~ 0.7%, is erf(x) = [1 - exp (- 4x2t)]1/2