title: Hohenberg-Kohn theorems in electrostatic and uniform magnetostatic fields.
abstract: The Hohenberg-Kohn (HK) theorems of bijectivity between the external scalar potential and the gauge invariant nondegenerate ground state density, and the consequent Euler variational principle for the density, are proved for arbitrary electrostatic field and the constraint of fixed electron number. The HK theorems are generalized for spinless electrons to the added presence of an external uniform magnetostatic field by introducing the new constraint of fixed canonical orbital angular momentum. Thereby, a bijective relationship between the external scalar and vector potentials, and the gauge invariant nondegenerate ground state density and physical current density, is proved. A corresponding Euler variational principle in terms of these densities is also developed. These theorems are further generalized to electrons with spin by imposing the added constraint of fixed canonical orbital and spin angular momenta. The proofs differ from the original HK proof and explicitly account for the many-to-one relationship between the potentials and the nondegenerate ground state wave function. A Percus-Levy-Lieb constrained-search proof expanding the domain of validity to N-representable functions, and to degenerate states, again for fixed electron number and angular momentum, is also provided.
authors.affiliation: Department of Physics, Ningbo University, Ningbo 315211, China.
authors.forename: Xiao-Yin
authors.initials: XY
authors.lastname: Pan
authors.affiliation: Brooklyn College and The Graduate School of the City University of New York, 365 Fifth Avenue, New York, New York 10016, USA.
authors.forename: Viraht
authors.initials: V
authors.lastname: Sahni