  Two pictures of BPS bound states in Calabi-Yau compactifications of type II
string theory exist, one as a set of particles at equilibrium separations from
each other, the other as a fusion of D-branes at a single point of space. We
show how quiver quantum mechanics smoothly interpolates between the two, and
use this, together with recent mathematical results on the cohomology of quiver
varieties, to solve some nontrivial ground state counting problems in
multi-particle quantum mechanics, including one arising in the setup of the
spherical quantum Hall effect, and to count ground state degeneracies of
certain dyons in supersymmetric Yang-Mills theories. A crucial ingredient is a
non-renormalization theorem in N=4 quantum mechanics for the first order part
of the Lagrangian in an expansion in powers of velocity.
