Applications of diffusion equation to the analysis in medical science

Abstract

The diffusion equation, which describes the time development of diffusion, is applied to wave function problem in quantum physics and to social problem in human science. From the comparison between the fundamental equations in different fields, we make a generalization to the original form of diffusion equation. Starting from the fundamental equation we calculate the predicted distribution for age distribution of three-disease population. Starting from the same equation, we obtain the Schrodinger equation through Wick's rotation. We solve the Schrodinger equation with non-linear potentials by the Monte Carlo method and show the solved wave functions. It is shown that the comparison of two applications is important since we notice the meaning of the parameters and quantities in the equations by the comparison of two applications, and since we can obtain new ideas through the discussions with the researchers in other fields.