  We show the feasibility of tensor network solutions for lattice gauge
theories in Hamiltonian formulation by applying matrix product states
algorithms to the Schwinger model with zero and non-vanishing fermion mass. We
introduce new techniques to compute excitations in a system with open boundary
conditions, and to identify the states corresponding to low momentum and
different quantum numbers in the continuum. For the ground state and both the
vector and scalar mass gaps in the massive case, the MPS technique attains
precisions comparable to the best results available from other techniques.
