Kato theorem

[1][2] It states that for generalized Coulomb potentials, the electron density has a cusp at the position of the nuclei, where it satisfies Here

For a Coulombic system one can thus, in principle, read off all information necessary for completely specifying the Hamiltonian directly from examining the density distribution.

This is also known as E. Bright Wilson's argument within the framework of density functional theory (DFT).

From Kato's theorem, one also obtains the nuclear charge of the nuclei, and thus the external potential is fully defined.

This is valid in a non-relativistic treatment within the Born–Oppenheimer approximation, and assuming point-like nuclei.