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Electron Density

  1. Dec 17, 2015 #1
    Hi
    I'd like to ask you about interpretation of electron density definition. According to the "Handbook of Molecular Physics and Quantum Chemistry" it goes like:

    ##\rho (\textbf{r})=N \sum_{\sigma_1}^{\sigma_N} \idotsint_{\mathbb{R^3}} |\psi_V (\textbf{r}_1, \sigma_1;\dots ;\textbf{r}_N,\sigma_N)|^2 d^3\textbf{r}_2 \dots d^3\textbf{r}_N##

    I know that my question may be a little imprecise so please - be patient. I'd like to know how to iterpret this definition. Why in the integral is only ##d^3\textbf{r}_2 \dots d^3\textbf{r}_N## but no ##d^3\textbf{r}_1d^3\textbf{r}_2 \dots d^3\textbf{r}_N##. How to explain this equation using physical viewpoint and how to explain it methematically ?

    Feel free to add any helpful information to understand this definition.
    Thanks in advance.
     
  2. jcsd
  3. Dec 17, 2015 #2
    Is your [tex] \rho(r) [/tex] supposed to be [tex] \rho(r_1) [/tex]?

    You have to leave at least one position variable un-integrated if you want the result to be a function of position. I think that's why.
     
  4. Dec 17, 2015 #3
    Ok, thank you for answer.
    I think this ##\rho(r)## should be ##\rho(r_1)##
    Can you tell me how it works mathematically?
    I need to have a function of position, I know that I can't to integrate every position (then it would be only a number). But how exactly it looks. Let's consider simple example of function ##f(x,y)## what would happen if I integrate it like this: ##\int f(x,y)dy=?##. The result for this example would be ##?=g(x)\times <number>##?
    Is it true in general case?
    Perhaps it is obvious but I really like to simplyfy everything and I'd like to be sure.
     
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