  The join $X\vee Y$ of two graphs $X$ and $Y$ is the graph obtained by joining
each vertex of $X$ to each vertex of $Y$. We explore the behaviour of a
continuous quantum walk on a weighted join graph having the adjacency matrix or
Laplacian matrix as its associated Hamiltonian. We characterize strong
cospectrality, periodicity and perfect state transfer (PST) in a join graph. We
also determine conditions in which strong cospectrality, periodicity and PST
are preserved in the join. Under certain conditions, we show that there are
graphs with no PST that exhibits PST when joined by another graph. This
suggests that the join operation is promising in producing new graphs with PST.
Moreover, for a periodic vertex in $X$ and $X\vee Y$, we give an expression
that relates its minimum periods in $X$ and $X\vee Y$. While the join operation
need not preserve periodicity and PST, we show that $\big| |U_M(X\vee
Y,t)_{u,v}|-|U_M(X,t)_{u,v}| \big|\leq \frac{2}{|V(X)|}$ for all vertices $u$
and $v$ of $X$, where $U_M(X\vee Y,t)$ and $U_M(X,t)$ denote the transition
matrices of $X\vee Y$ and $X$ respectively relative to either the adjacency or
Laplacian matrix. We demonstrate that the bound $\frac{2}{|V(X)|}$ is tight for
infinite families of graphs.
