  We compute the Witten index of one-dimensional gauged linear sigma models
with at least ${\mathcal N}=2$ supersymmetry. In the phase where the gauge
group is broken to a finite group, the index is expressed as a certain residue
integral. It is subject to a change as the Fayet-Iliopoulos parameter is varied
through the phase boundaries. The wall crossing formula is expressed as an
integral at infinity of the Coulomb branch. The result is applied to many
examples, including quiver quantum mechanics that is relevant for BPS states in
$d=4$ ${\mathcal N}=2$ theories.
