Abstract
The optimizing Euler equations for the dynamic linear-response function are derived starting from the Jastrow ansatz for the wave function and including also the backflow effect. The elementary excitations in liquid He4 are calculated consistently using the hypernetted-chain approximation for the uniform system as well as for weakly disturbed static and dynamic systems. The resulting excitation-energy spectrum is found to agree well with experiments up to the maxon region giving a maxon energy of 14.05 K and a roton energy of 11.7 K.