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## Main Question or Discussion Point

Hello! I am really new to this field, so I am sorry if my questions is silly or missing some parts. Please correct me if that is so. I am a bit confused about how well we can extract the value of a transition, say from ground to an excited state, of an atom (let's assume we can ignore any other energy levels, other than the probed ones i.e. 2 level system). Assume that we fit a Gaussian (it can be a Lorentzian or Voigt too) profile to our data (say we scan the frequency range with a laser) and from the fit we get a value for the center frequency of 100 and an error on the center (from the fitting program itself, which can be a chi-square minimization) of 3. Assume that the errors come only from the counting (i.e. Possion errors) and we have no systematics. Also assume that the sigma of the gaussian from the fit is 15 (due to Doppler thermal broadening). How well do we know the value of the transition? Would it be ##100 \pm 15## or ##100 \pm 3## or does it depends on other factors too? Also, assuming we reduce the temperature a lot and reach the natural width which is known to be (from theory or somehow else) 5, but we get an error on the fitting procedure of 3 again. Does it mean that we constrained the central value better than the natural linewidth? Is this even possible? So mainly, can someone explain to me how do we define the error on the measured transition given an experiment (and what other parameters that I miss we should take into account)? Thank you!