 While the standard deviation is the most well-known quantitative measure for uncertainty or the spread in the probability distribution, it is not the only one, and indeed it has distinctive drawbacks that other such measures may lack. For example, in the definition of the standard deviations  (11)  one can see that that the probability density function  \(\abs{\psi(q)}^2\) is weighed by a quadratic factor \(q^2\) that puts increasing emphasis on its tails. Therefore, the value of \(\Delta_\psi \bQ\) will depend predominantly at how this density behaves at the tails: if these falls off very quickly, e.g., like a Gaussian, it will be small, but if the tails drop off only slowly the standard deviation may be very large, even when most probability is concentrated in a small interval.