The position and momentum operators are hermitian. Since the position and momentum operators do not commute, one can not find simultaneous eigenstates of both of the operators. (We also know this because the eigenvectors of the position operator are delta functions, and the eigenvectors of the momentum operator are plane waves.) The uncertainty principle states that the root mean square deviation from average in the position (Delta x) times the root mean square deviation from average in the momentum (Delta p) is greater than or equal to hbar/s. There will be a similar uncertaintly relation for any two operators which do not commute. A particular form of a gaussian wave function is a minimum uncertaintly wave function: (Delta x)(Delta p) = hbar/2.