Distribution of Vibrational Frequencies of a Crystal by Fourier Transformation of the Heat Capacity

摘要

It is shown that when represented on a logarithmic temperature scale a thermodynamic function is theresultantor convolution of the frequency distribution function and a function characteristic of a single oscillator. The inversion to yield the frequency distribution function may be accomplished by means of a theorem on the Fourier transform of a resultant. The method is related to that of Montroll, but may be in a more practical form for calculation. The present formulation also yields a quantitative expression for the error in the frequency distribution function which shows the importance of adequate smoothing of the experimental data.