  We investigate the dynamics of the eigenstate of an infinite well under an
abrupt shift of the well's wall. It is shown that when the shift is small
compared to the initial well's dimensions, the short time behavior changes from
the well known t^(3/2) behavior to t^(1/2) . It is also shown that the complete
dynamical picture converges to a universal function, which has fractal
structure with dimensionality D=1.25.
