  The multi-electron wave function of an interacting electron system depends on
the size of the system, i.e. the number of electrons. Here the question
investigated is how the wave function changes for a symmetric Friedel-Anderson
impurity when the volume is doubled. It turns out that for sufficiently large
volume (when the level spacing is smaller than the resonance width) the change
in the wave function can be expressed in terms of a universal single-electron
state |q> centered at the Fermi level. This electron state is independent of
the number of electrons and independent of the parameters of the
Friedel-Anderson impurity. It is even the same universal state for a Kondo
impurity and a symmetric Friedel impurity independent of any parameter. The
only requirement is that the impurity has a resonance exactly at the Fermi
level and that the level spacing is smaller than the resonance width. This
result clarifies recent fidelity calculations.
