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We suggest a new method to compute the spectrum and wave functions of excitedstates. We construct a stochastic basis of Bargmann link states, drawn from aphysical probability density distribution and compute transition amplitudesbetween stochastic basis states. From such transition matrix we extract wavefunctions and the energy spectrum. We apply this method to $U(1)_{2+1}$ latticegauge theory. As a test we compute the energy spectrum, wave functions andthermodynamical functions of the electric Hamiltonian and compare it withanalytical results. We find excellent agreement. We observe scaling of energiesand wave functions in the variable of time. We also present first results on asmall lattice for the full Hamiltonian including the magnetic term.

Spectrum and Wave Functions of Excited States in Lattice Gauge Theory