  Quantum walks are considered to be quantum counterparts of random walks.They
show us impressive probability distributions which are different from those of
random walks.That fact has been precisely proved in terms of mathematics and
some of the results were reported as limit theorems.When we analyze quantum
walks, some conventional methods are used for the computations.Especially, the
Fourier analysis has played a role to do that.It is, however, compatible with
some types of quantum walks (e.g. quantum walks on the line with a spatially
homogeneous dynamics) and can not well work on the derivation of limit theorems
for all the quantum walks.In this paper we try to obtain a limit theorem for a
quantum walk on the half line by the usage of the Fourier analysis.Substituting
a quantum walk on the line for it, we will lead to a possibility that the
Fourier analysis is useful to compute a limit distribution of the quantum walk
on the half line.
