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Random phase (?) approximation

  1. Apr 15, 2014 #1
    Hello,
    I've come across equations where people use the approximation

    [tex] \int_0^1 \exp(f(x))\, dx \approx \exp \left( \int_0^1 f(x)\, dx\right) [/tex]

    I can see that this is correct if f(x) is small, one just uses exp(x) = 1+x+...
    However, it appears that this approximation has a broader validity that that... How is it called (Random phase approximation??) and where could I find more info about it?
     
  2. jcsd
  3. Apr 16, 2014 #2
    I've seen something similar used in mean field theory to estimate the partition function of some difficult to calculate system. I think the particular step that reminds me of your equation is called the Bogoliubov Inequality.
     
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