In this paper, we present a numerical investigation about the question how sensitively Fourier coefficients of the positron wave function ψ_{+} react to different (and not too strong) changes of ψ_{+}. In order to obtain general information about this problem, we studied this sensitivity for several bcc and fcc metals and for different models of the positron wave function. Summarizing our results, we can say that this sensitivity is generally small (or at least moderate) for Fourier coefficients belonging to reciprocal lattice vectors G which lie nearest to the centre of the momentum space. For the outer vectors G, the amount of this sensitivity is strongly dependent on the crystal structure of the metal and on the special like of the change of the positron wave function.