A Trial Generator Function Common for Charge and Momentum Density Distributions in Valence Electron System in Solid

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  • Trial Generator Function Common for Charge and Momentum Density Distributions in Valence Electron System in Solid
  • 固体価電子系の電荷密度および運動量密度分布関数に対する共通母関数誘導の試み

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In a valence electron system of solid, the density distribution functions of electron charge and electron momentum are the functions described in terms of the electron wave functions in the real and the momentum spaces, respectively. The former density n(r) is a local function of the electron coordinate variable r and the latter density p(q) is one of the local momentum variable q. While the two kinds of wave functions are connected with each other through the Fourier transformation mathematically, there is no mathematical operation to transform the one of the distribution functions to the other directly. In this note, by using the fact that the function p(q) can be Fourier-transformed into a form of autocorrelative function composed of nonlocal terms of the electron wave function with respect to the variable r, a trial generating relation is proposed for connecting the two kinds of density distribution function. The generator function is a very simple and formal one, but gives a step in fair prospects for mathematical structure between the two different kinds of density distribution function in a unified framework.

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