  We use an one dimensional model of a square barrier embedded in an infinite
potential well to demonstrate that tunneling leads to a complex behavior of the
wave function and that the degree of complexity may be quantified by use of the
spatial entropy function defined by S = -\int |\Psi(x,t)|^2 ln |\Psi(x,t)|^2
dx. There is no classical counterpart to tunneling, but a decrease in the
tunneling in a short time interval may be interpreted as an approach of a
quantum system to a classical system. We show that changing the square barrier
by increasing the height/width do not only decrease the tunneling but also
slows down the rapid rise of the entropy function, indicating that the entropy
growth is an essentially quantum effect.
