Abstract
Phonons in a crystalline solid and a dilute Bose gas are treated from a uniform point of view. In each of the cases, the potential is expanded about ionic (or atomic) ‘equilibrium’ positions, with the important difference that in the gaseous state these positions are allowed to move. This motion leads to an additional term in the kinetic energy part of the gas Hamiltonian, resulting in a dispersion relation for long wavelength density fluctuations identical to that obtained by Bogoliubov. The usual lattice phonon spectrum is also reproduced. The limitations of the viewpoint when applied to liquids and Fermi gases are discussed.
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