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Closed-form solution for inverse problems of Fermi systems.

A series of applications of a theorem relating the Dirac \ensuremath{\delta} function to the Fermi distribution [Chen, Phys. Rev. A 46, 3538 (1992)] are presented in this paper. In particular, the inverse problem for determining the density of states of Fermi systems, the determination of relaxation-time distribution from dielectric function spectra, and the inverse isotherm problem for the adsorption energy distribution function are treated with closed-form general solutions. The present method is not only simplified significantly relative to all the previous work, but also has the merit of not making priori assumptions about the solution of the integral equation; hence it is a direct way of evaluating the density of states.