The main assumption in the Thomas–Fermi model is that there is an internal chemical potential at each point r that depends only on the electron concentration at the same point r. This behaviour cannot be exactly true because of the Heisenberg uncertainty principle. No electron can exist at a single point; each is spread out into a wavepacket of size ≈ 1 / k F, where k F is the Fermi wavenumber, i.e. a typical wavenumber for the states at the Fermi surface. Therefore, it cannot be possible to define a chemical potential at a single point, independent of the electron density at nearby points.