Inversion of the Partition Function to Determine the Density of Energy States

Abstract

The density of energy states for a complex system may be deduced from thermodynamic functions when their dependence on temperature is specified. The method is general and depends for its accuracy on the closeness of approximation of the experimentally determined partition function by an appropriate equation. Accurate specific heat data are therefore essential. The degeneracy function is obtained by inverting the Laplace integral defining the sum‐over‐states; as illustrations, the energy states for an Einstein crystal, and for a modified Debye crystal without and with a transition are discussed. The author was not successful in finding a mathematical expression which fitted the last case sufficiently well to differentiate between transitions of first and higher order.