## Abstract

The solid hydrogens, together with solid He^{4} and He^{3}, form a class of solids known as *quantum crystals*. These solids are characterized by the property that the amplitude of the zero-point lattice vibrations is an appreciable fraction of the lattice constant, as a result of the small mass of the molecules and the relatively weak intermolecular forces. In a normal crystal the lattice vibrations can be treated by expanding the potential energy in powers of the displacements of the molecules from their equilibrium positions, but in quantum crystals this procedure leads to imaginary phonon frequencies in at least part of the BZ, and must be replaced by a *self-consistent phonon formalism* not based on an expansion in powers of the displacements. Only the main concepts of the theory of quantum crystals are discussed here, and for further details we refer to the available reviews.^{1, 2} The elastic properties of a solid are closely related to the long-wavelength phonon modes, and a generalized Debye model, parameterized in terms of the elastic constants, is introduced to describe the anisotropy in the propagation and polarization properties of the phonon modes in hcp solid H_{2} and D_{2}. This model is useful for calculating certain properties of these solids depending on the anisotropy of the phonon field.

## Keywords

Coherent State Lattice Vibration Harmonic Approximation Solid Hydrogen Quantum Crystal## Preview

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