A representation of the exact nonlocal exchange-potential operator is propo
sed and applied to study electron-impact vibrational excitation of H-2 in t
he low- and intermediate-energy range. In our approach. a complete set of o
ne-dimensional particle-in-box wave functions is used as expansion basis. T
his representation of the exchange operator is easy to program and the calc
ulated cross sections converge rapidly with the number of basis functions.
Excitation cross sections for the transitions v' = 0 --> v = 0, 1, 2, and 3
calculated in the 1.5-100-eV range are in general good agreement with the
available experimental and theoretical data.