# Physics 434, 2014: Homework 3

5. Calculate the drift and the diffusion constants for a random walk on a lattice with a lattice spacing of ${\displaystyle a}$, where particles hop between the sites every ${\displaystyle \Delta t}$ units of time, and they have a probability of ${\displaystyle p}$ going left, and ${\displaystyle q=1-p}$ going right. What are these quantities if the particle goes to the left with the probability ${\displaystyle p}$, to the right with ${\displaystyle q}$, and stays in place with the probability ${\displaystyle r=1-p-q}$?