  We demonstrate the control of the dispersion of matter wave packets utilizing
periodic potentials. This is analogous to the technique of dispersion
management known in photon optics. Matter wave packets are realized by
Bose-Einstein condensates of 87Rb in an optical dipole potential acting as a
one-dimensional waveguide. A weak optical lattice is used to control the
dispersion relation of the matter waves during the propagation of the wave
packets. The dynamics are observed in position space and interpreted using the
concept of effective mass. By switching from positive to negative effective
mass, the dynamics can be reversed. The breakdown of the approximation of
constant, as well as experimental signatures of an infinite effective mass are
studied.
