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Hohenberg-Kohn Theorems in Electrostatic and Uniform Magnetostatic Fields
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
momentum. 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.Comment: 16 pages; 1 Tabl
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