  We have evaluated the angular-momentum distribution functions for finite
numbers of electrons in Laughlin states. For very small numbers of electrons
the angular-momentum state occupation numbers have been evaluated exactly while
for larger numbers of electrons they have been obtained from Monte-Carlo
estimates of the one-particle density matrix. An exact relationship, valid for
any number of electrons, has been derived for the ratio of the occupation
numbers of the two outermost orbitals of the Laughlin droplet and is used to
test the accuracy of the MC calculations. We compare the occupation numbers
near the outer edges of the droplets with predictions based on the chiral
Luttinger liquid picture of Laughlin state edges and discuss the surprisingly
large oscillations in occupation numbers which occur for angular momenta far
from the edge.
