Procedures for basic inverse problems: Black body radiation problem and phonon density of states problem.

Abstract

Two numerical procedures, the regularization method and the maximum entropy method, have been investigated and developed to solve some basic inverse problems in theoretical physics. Both of them are applied to the inverse black body radiation problem and the inverse phonon density of states problem. The inverse black body radiation problem is concerned with the determination of the area temperature distribution of a black body source from spectral measurements of its radiation. The phonon density of states problem is defined to be the determination of the phonon density of states function from the measured lattice specific heat function at constant volume. Those problems are ill-posed and can be expressed as a Fredholm integral equation of the first kind. It appears that both the regularization method and the maximum entropy method are successful in solving the two ill-posed problems. Generally the two procedures can be applied to any inverse problem which belongs to the class of the Fredholm integral equation of the first kind.