  We consider the temporal evolution of a zero energy edge Majorana of a
spinless $p$-wave superconducting chain following a sudden change of a
parameter of the Hamiltonian. Starting from one of the topological phases that
has an edge Majorana, the system is suddenly driven to the other topological
phase or to the (topologically) trivial phases and also to the quantum critical
points (QCPs) separating these phases. The survival probability of the initial
edge Majorana as a function of time is studied following the quench.
Interestingly when the chain is quenched to the QCP, we find a nearly perfect
oscillations of the survival probability, indicating that the Majorana travels
back and forth between two ends, with a time period that scales with the system
size. We also generalize to the situation when there is a next-nearest-neighbor
hopping in superconducting chain and there resulting in a pair of edge Majorana
at the each end of the chain in the topological phase. We show that the
frequency of oscillation of the survival probability gets doubled in this case.
We also perform an instantaneous quenching the Hamiltonian (with two Majorana
modes at each end of the chain) to an another Hamiltonian which has only one
Majorana mode in equilibrium; the MSP shows oscillations as a function of time
with a noticeable decay in the amplitude. On the other hand for a quenching
which is reverse to the previous one, the MSP decays rapidly and stays close to
zero with fluctuations in amplitude.
