  We investigated the discrete-time quantum random walks on a line in periodic
potential. The probability distribution with periodic potential is more complex
compared to the normal quantum walks, and the standard deviation $\sigma$ has
interesting behaviors for different period $q$ and parameter $\theta$. We
studied the behavior of standard deviation with variation in walk steps,
period, and $\theta$. The standard deviation increases approximately linearly
with $\theta$ and decreases with $1/q$ for $\theta\in(0,\pi/4)$, and increases
approximately linearly with $1/q$ for $\theta\in[\pi/4,\pi/2)$. When $q=2$, the
standard deviation is lazy for $\theta\in[\pi/4+n\pi,3\pi/4+n\pi],n\in Z$.
