The differential neutron flux in slab geometry can be represented as a linear combination of traveling eigenmodes that propagate with exponential decay as functions of distance. The operators that serve to analyze the flux into mode amplitudes and to synthesize the flux from the mode amplitudes are determined. The particular analyzers and synthesizers it is appropriate to use in any given situation depend on the boundary conditions. These operators have an interpretation independent of any particular problem. The fluxes of interest can be written down almost by inspection in terms of these operators.