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Notation for Fourier transforamtion

$\displaystyle f({\bf r}) = \int e^{i{\bf kr}} f_k \frac{d{\bf k}}{(2\pi)^3}$

(5.1)

$\displaystyle f_k = \int e^{-i{\bf kr}} f({\bf r}) d{\bf r}$

(5.2)

$\displaystyle \delta{\bf k} = \int e^{i{\bf kr}} d{\bf r}$

(5.3)

$\displaystyle \int \delta {\bf k} \frac{d{\bf k}}{(2\pi)^3} = 1$

(5.4)