Simple series solutions to specific heat-phonon spectrum inversion

TL;DR

This paper introduces a simple series method for inverting the specific heat-phonon spectrum and black-body radiation problems, making calculations easier for these inherently ill-posed issues in solid physics.

Contribution

A novel, straightforward series solution approach for the ill-posed specific heat-phonon spectrum inversion and black-body radiation inversion problems.

Findings

Series solutions are easily computed from power or asymptotic expansions.

Method simplifies the inversion process for specific heat and radiation spectra.

Applicable to problems with ratio expansions of specific heat or asymptotic forms.

Abstract

The specific heat-phonon spectrum inversion has played a significant role in solid physics. But for this inherently ill-posed problem, most of the known solutions are complex both in form and content, although they are rigorous and perfect. Here we suggest another simpler series solution to this problem, which can be easily calculated if the ratio of specific heat to temperature can be expanded into a power series, or specific heat can be expanded asymptotically and conditionally. Furthermore, we suggest similar solutions to the black-body radiation inversion.