Motivation

We want to solve Schrödinger's equation:

$$-{\textstyle{1 \over 2}} \nabla^2 \psi({\bf r}) + V({\bf r}) \psi({\bf r}) = \varepsilon \psi({\bf r})$$

• Kinetic energy operator is diagonal in momentum-space
• Potential operator is diagonal in real-space

$\Rightarrow$ need to be able to switch between momentum- and real-space representations i.e. perform Fourier transforms.