  In this paper, we study the time evolution of the expectation value of
Majorana neutrino with the Schr\"odinger picture.The operators with the
definite lepton number and operators with the definite mass are related to each
other by a Bogolyubov transformation. Then the vacuum with the null lepton
number is also related to the vacuum for the massive operator and it is written
by the superposition of the vacuum for massive field and Majorana pairs
condensed states. We choose the state with a definite lepton number $L$ $=1$
and the momentum ${\bf q}\ne 0$ as an initial state. By writing the state in
terms of the superposition of energy eigenstates, we are able to study the time
evolution of the state in the Schr\"odinger picture.The expectation value of
lepton number operator is computed and it reproduces the same result as that
obtained in the corresponding Heisenberg operator.
