Overview
The 3 dimensional Fourier Transform is applicable to functions of three variables, typically used to analyze functions of 3-d space, using the variables {% x %},{% y %},and {% z %}. (alternately {% x_1 %},{% x_2 %},{% x_3 %}) which are gathered together into a vector, {% \vec{x} %}.
{% \psi(\vec{x}) = (2 \pi)^{-\frac{3}{2}} \int \phi(\vec{k}) e^{i \vec{k} \cdot \vec{x}} d^3 \vec{k} %}
{% \phi(\vec{k}) = (2 \pi)^{-\frac{3}{2}} \int \psi(\vec{x}) e^{-i \vec{k} \cdot \vec{x}} d^3 \vec{x} %}