Generalization of the Hohenberg–Kohn theorem to the presence of a magnetostatic field Original Research Article

The Hohenberg–Kohn theorem is generalized to the case of electrons in the presence of both an external electrostatic E(r)=−∇v(r)E(r)=−∇v(r) and magnetostatic B(r)=∇×A(r)B(r)=∇×A(r) field. For the non-degenerate ground state, it is established that the basic variables are the ground state density ρ(r)ρ(r) and physical current density j(r)j(r) by proving the relationship between the densities {ρ(r),j(r)}{ρ(r),j(r)} and the external potentials {v(r),A(r)}{v(r),A(r)} is one-to-one . A constrained-search proof is also provided. It is further explained why the basic variables cannot be the density ρ(r)ρ(r) and the paramagnetic current density jp(r)jp(r) as presently thought to be the case.