  In this work, we present a stochastic variational calculation (SVM) of
energies and wave functions of few particle systems coupled to quantum fields
in cavity QED. The light-matter coupled system is described by the Pauli-Fierz
Hamiltonian. The spatial wave function and the photon spaces are optimized by a
random selection process. Examples for a two-dimensional trion and confined
electrons as well as for the He atom and the Hydrogen molecule are presented
showing that the light-matter coupling drastically changes the electronic
states.
