Extended Lagrangian Born-Oppenheimer molecular dynamics [A. M. N. Niklasson, Phys. Rev. Lett. 100, 123004 (2008)] has been generalized to the propagation of the electronic wave functions. The technique allows highly efficient first principles molecular dynamics simulations using plane wave pseudopotential electronic structure methods that are stable and energy conserving also under incomplete and approximate self-consistency convergence. An implementation of the method within the plane-wave basis set is presented and the accuracy and efficiency is demonstrated both for semiconductor and metallic materials.