Modified Mobius inverse formula and its applications in physics

A new theorem of inverse formula is introduced for a kind of infinite series. Thus some new results for important inverse problems in physics are presented in this paper. These are the inverse problems for obtaining the photon density of states, the inverse blackbody radiation problem for remote sensing, and the solution for inverse Ewald summation. Of more importance, it shows the possibility of the application of number theory to physical problems. 1 G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers (Oxford Univ. Press, Oxford, 1979), 5th ed.