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In this paper, we study the time evolution of the expectation value ofMajorana neutrino with the Schr\"odinger picture.The operators with thedefinite lepton number and operators with the definite mass are related to eachother by a Bogolyubov transformation. Then the vacuum with the null leptonnumber is also related to the vacuum for the massive operator and it is writtenby the superposition of the vacuum for massive field and Majorana pairscondensed 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 interms of the superposition of energy eigenstates, we are able to study the timeevolution of the state in the Schr\"odinger picture.The expectation value oflepton number operator is computed and it reproduces the same result as thatobtained in the corresponding Heisenberg operator.

Time evolution of the lepton number of Majorana neutrinos in the Schr\"odinger picture versus Heisenberg picture