  We suggest a new method to compute the spectrum and wave functions of excited
states. We construct a stochastic basis of Bargmann link states, drawn from a
physical probability density distribution and compute transition amplitudes
between stochastic basis states. From such transition matrix we extract wave
functions and the energy spectrum. We apply this method to $U(1)_{2+1}$ lattice
gauge theory. As a test we compute the energy spectrum, wave functions and
thermodynamical functions of the electric Hamiltonian and compare it with
analytical results. We find excellent agreement. We observe scaling of energies
and wave functions in the variable of time. We also present first results on a
small lattice for the full Hamiltonian including the magnetic term.
