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We consider the linear Schrödinger equation and its discretization by splitstep methods where the part corresponding to the Laplace operator is approximated by the midpoint rule. We show that the numerical solution coincides with the exact solution of a modified partial differential equation at each time step. This shows the existence of a modified energy preserved by the numerical scheme. This energy is close to the exact energy if the numerical solution is smooth. As a consequence, we givedoi:10.1137/080744578 fatcat:ikregeybafdqzbzfnhuyw26tsa