For a Bose system interacting through a two-body potential there is a large occupation number in the zero-momentum state with small fluctuations. Thus, we can express the chemical potential and low-lying excitation energy in terms of the density fluctuation only. The formulas derived are shown to coincide with well-established results in the low-density Bose gas. The use of experimental neutron scattering data is suggested to improve the numerical answer. A particular application is made to the
He4 case. If we utilize the Feynman variational excited state as the (approximate) true state vector, which is correct experimentally for low-momentum excitations, we get an explicit phonon excitation for actual
He4.
We continue the analysis of the one-dimensional gas of Bose particles interacting via a repulsive delta function potential by considering the excitation spectrum. Among other things we show that: (i) the elementary excitations are most naturally thought of as a double spectrum, not a single one; (ii) the velocity of sound derived from the macroscopic compressibility is shown to agree with the velocity of sound derived from microscopic considerations, i.e., from the phonon spectrum. We also introduce a distinction between elementary excitations and quasiparticles, on the basis of which we give some heuristic reasons for expecting the double spectrum to be a general feature, even in three dimensions, and not an exception.