Theory of inhomogeneous quantum systems. II. Linear response and collective excitations in Bose systems

We generalize the variational theory of inhomogeneous Bose systems (presented in the preceding paper) to study collective excitations and the linear response to an external perturbing field. As a by-product of the optimized treatment of the ground state, we obtain dispersion relations and wave shapes for the spectrum of the ripplons and phonons. Results are presented for the surface and volume excitations of free films of ${}_{}{}^4{}_{}{}^{}\mathrm{He}$. At wave numbers corresponding to the location of the roton minimum in bulk ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ we find a level crossing between surface and volume excitations.