  We discuss a new numerical method for the determination of excited states of
a quantum system using a generalization of the Feynman-Kac formula. The method
relies on introducing an ensemble of non-interacting identical systems with a
fermionic statistics imposed on the systems as a whole, and on determining the
ground state of this fermionic ensemble by taking the large time limit of the
Euclidean kernel. Due to the exclusion principle, the ground state of an
$n$-system ensemble is realized by the set of individual systems occupying
successively the $n$ lowest states, all of which can therefore be sampled in
this way. To demonstrate how the method works, we consider a one-dimensional
oscillator and a chain of harmonically coupled particles.
