The linear response function x(r,r): another perspective

In this paper, we propose a conceptual approach to assign a "mathematical meaning "to the non-local function chi(r,r '). Mathematical evaluation of this kernel remains difficult since it is a function depending on six Cartesian coordinates. The idea behind this approach is to look for a limit process in order to explore mathematically this non-local function. According to our approach, the bra ,the value < r '|psi >. In condensed writing =< r '|psi >, and this is achieved by exploiting the sifting property of the delta function that gives it the sense of a measure, i.e. measuring the value of psi(r)at the pointr '.It isworth noting that 0. In thisregard,chi(xi)(r ')(r)acts as a limit of an integral operator kernel in a convolution integration procedure.