  We derive a relation between leading finite size corrections for a 1+1
dimensional quantum field theory on a strip and scattering data, which is very
similar in spirit to the approach pioneered by Luscher for periodic boundary
conditions. The consistency of the results is tested both analytically and
numerically using thermodynamic Bethe Ansatz, Destri-de Vega nonlinear integral
equation and classical field theory techniques. We present strong evidence that
the relation between the boundary state and the reflection factor one-particle
couplings, noticed earlier by Dorey et al. in the case of the Lee-Yang model
extends to any boundary quantum field theory in 1+1 dimensions.
