We calculate the stationary wave functions for two identical particles
in a common one-dimensional potential well and interaction through a
repulsive delta-potential. We show how a symmetric noninteracting stat
e psi(m,n)((+)), where the particles occupy the single-particle orbita
ls m and n, evolves as a function of the interaction strength. In the
limit of very strong repulsion, the energy levels coincide with those
for the adjacent antisymmetric states psi(m,n+1)((-)). The spatial pro
bability distributions also coincide, revealing an apparent change of
statistics. However, the relative momentum wave functions are differen
t demonstrating memory of original statistics. (C) 1998 American Assoc
iation of Physics Teachers.