  We consider the stationary state of a quantum walk on the finite path, where
the sink and source are set at the left and right boundaries. The quantum coin
is uniformly placed at every vertex of the path graph. At every time step, a
new quantum walker penetrates into the internal from the left boundary and also
some existing quantum walkers in the internal goes out to the sinks located in
the left and right boundaries. The square modulus of the stationary state at
each vertex is regarded as the comfortability for a quantum walker to this
vertex in this paper. We show the weak convergence theorem for the scaled limit
distribution of the comfortability in the limit of the length of the path.
