 Both the standard deviation and the alternative measures of uncertainty considered in the previous subsection (and many more that we have not mentioned!) are designed to indicate the width or spread of a single given probability distribution. Applied to quantum mechanics, where the probability distributions for position and momentum are obtained from a given quantum state vector, one can use them to formulate uncertainty relations that characterize the spread in those distribution for any given state. The resulting inequalities then express limitations on what state-preparations quantum mechanics allows. They are thus expressions of what may be called a preparation uncertainty principle: