= Symmetric exponential excitation pulse
{title2=$f(t)=e^{-b|t|}$}
For $b>0$, the <Fourier transform> of $f$ is $\int_{-\infty}^{\infty}f(t)e^{ixt}dt=2b/(b^2+x^2)$. A weak interaction $D_0f(t)\cos\omega t$ between <energy levels> of gap $\hbar\omega_0$ gives final <probability amplitude> $-idb\{[b^2+(\omega_0-\omega)^2]^{-1}+[b^2+(\omega_0+\omega)^2]^{-1}\}/\hbar$, where $d$ is the transition <matrix element>. Only when $b,|\omega_0-\omega|\ll\omega_0$ does the single resonant lobe give an approximately squared <Lorentzian line shape> excitation profile. Its <full width at half maximum> is $2b\sqrt{\sqrt2-1}$ in <angular frequency>.
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