Abstract
Quantization of the hydrodynamic modes in superfluid He4 with a free surface is carried out. A complete and orthonormal set of eigenfunctions for both ripplons and surface-reflected phonons is constructed. Applications of the formalism to the calculation of the thermal energy density near the surface, the temperature-dependent part of the surface tension, and the rate at which power is absorbed by the surface from an incident phonon beam are given.