An approximate scheme to determine the vibratory density of states in a quasi-harmonic solid

In a new and realistic conception of solids, an analytical approach is presented to find the phonon density of states in a quasi-harmonic one-dimensional solid by starting from the fact that a solid with strong interatomic forces can be regarded as an atomic array of quantum anharmonic oscillators under a Morse potential. In fact, our quasi-harmonic approximation is derived by assuming a large enough solid with an involved anharmonic parameter as a sufficiently small quantity. In this context, a mathematical relationship between the above parameter and the matrix element relative to oscillator’s strength is obtained.