  We discuss nonspreading wave packets in one dimensional Schr\"{o}dinger
equation. We derive general rules for constructing nonspreading wave packets
from a general potential $\textmd{V}(x,t)$. The essential ingredients of a
nonspreading wave packet, the shape function $f(x)$, the motion $d(t)$, the
phase function $\phi(x,t)$ are derived. Since the form of the shape of a
nonspreading wave packet does not change in time, the shape equation should be
time independent. We show that the shape function $f(x)$ is the eigenfunction
of the time independent Schr\"{o}dinger equation with an effective potential
$V_{\textmd{eff}}$ and an energy $E_{\textmd{eff}}$. We derive nonspreading
wave packets found by Schr\"{o}dinger, Senitzky, and Berry and Balazs as
examples. We show that most stationary potentials can only support stationary
nonspreading wave packets. We show how to construct moving nonspreading wave
packets from time dependent potentials, which drive nonspreading wave packets
into an arbitrary motion.
