TCSA and the finite volume boundary state

We develop a new way to calculate the overlap of a boundary state with a finite volume bulk state in the truncated conformal space approach. We check this method in the thermally perturbed Ising model analytically, while in the scaling Lee-Yang model numerically by comparing our results to excited state g-functions, which we obtained by the analytical continuation method. We also give a simple argument for the structure of the asymptotic overlap between the finite volume boundary state and a periodic multiparticle state, which includes the ratio of Gaudin type determinants.