  We take a one-dimensional tight binding chain with periodic boundary
condition and put a particle in an arbitrary Bloch state, then quench it by
suddenly changing the potential of an arbitrary site. In the ensuing time
evolution, the probability density of the wave function at an arbitrary site
\emph{jumps indefinitely between plateaus}. This phenomenon adds to a former
one in which the survival probability of the particle in the initial Bloch
state shows \emph{cusps} periodically, which was found in the same scenario
[Zhang J. M. and Yang H.-T., EPL, \textbf{114} (2016) 60001]. The plateaus
support the scattering wave picture of the quench dynamics of the Bloch state.
Underlying the cusps and jumps is the exactly solvable, nonanalytic dynamics of
a Luttinger-like model, based on which, the locations of the jumps and the
heights of the plateaus are accurately predicted.
