  We derive analytical expressions for the single mode quantum field state at
the individual output ports of a beam splitter when a single-photon Fock state
and a coherent state are incident on the input ports. The output states turn
out to be a statistical mixture between a displaced Fock state and a coherent
state. Consequently we are able to find an analytical expression for the
corresponding Wigner function. Because of the generality of our calculations
the obtained results are valid for all passive and lossless optical four port
devices. We show further how the results can be adapted to the case of the
Mach-Zehnder interferometer. In addition we consider the case for which the
single-photon Fock state is replaced with a general input state: a coherent
input state displaces each general quantum state at the output port of a beam
splitter with the displacement parameter being the amplitude of the coherent
state.
