Hohenberg–Kohn theorem
E645114
The Hohenberg–Kohn theorem is a foundational result in quantum mechanics that establishes the ground-state electron density as the central quantity determining all properties of a many-electron system, forming the basis of density functional theory.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Hohenberg–Kohn theorem canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T7150595 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Hohenberg–Kohn theorem Context triple: [density functional theory, hasTheorem, Hohenberg–Kohn theorem]
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A.
Feynman–Hellmann theorem
The Feynman–Hellmann theorem is a result in quantum mechanics that relates the derivative of an energy eigenvalue with respect to a parameter in the Hamiltonian to the expectation value of the corresponding derivative of the Hamiltonian.
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B.
Bogoliubov–Parasyuk theorem
The Bogoliubov–Parasyuk theorem is a fundamental result in quantum field theory that rigorously establishes a systematic procedure for renormalizing divergent Feynman diagrams.
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C.
Gell-Mann–Low theorem
The Gell-Mann–Low theorem is a fundamental result in quantum field theory that rigorously connects interacting quantum fields to free fields via the adiabatic switching-on of interactions, underpinning the use of perturbation theory and the Dyson series.
-
D.
Hartree–Fock method
The Hartree–Fock method is an approximate quantum mechanical approach for determining the electronic structure of atoms, molecules, and solids by modeling electrons as occupying self-consistent single-particle orbitals.
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E.
Born–Oppenheimer approximation
The Born–Oppenheimer approximation is a fundamental method in molecular quantum mechanics that simplifies calculations by treating nuclear motion as much slower than electronic motion, allowing their behaviors to be separated.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Hohenberg–Kohn theorem Target entity description: The Hohenberg–Kohn theorem is a foundational result in quantum mechanics that establishes the ground-state electron density as the central quantity determining all properties of a many-electron system, forming the basis of density functional theory.
-
A.
Feynman–Hellmann theorem
The Feynman–Hellmann theorem is a result in quantum mechanics that relates the derivative of an energy eigenvalue with respect to a parameter in the Hamiltonian to the expectation value of the corresponding derivative of the Hamiltonian.
-
B.
Bogoliubov–Parasyuk theorem
The Bogoliubov–Parasyuk theorem is a fundamental result in quantum field theory that rigorously establishes a systematic procedure for renormalizing divergent Feynman diagrams.
-
C.
Gell-Mann–Low theorem
The Gell-Mann–Low theorem is a fundamental result in quantum field theory that rigorously connects interacting quantum fields to free fields via the adiabatic switching-on of interactions, underpinning the use of perturbation theory and the Dyson series.
-
D.
Hartree–Fock method
The Hartree–Fock method is an approximate quantum mechanical approach for determining the electronic structure of atoms, molecules, and solids by modeling electrons as occupying self-consistent single-particle orbitals.
-
E.
Born–Oppenheimer approximation
The Born–Oppenheimer approximation is a fundamental method in molecular quantum mechanics that simplifies calculations by treating nuclear motion as much slower than electronic motion, allowing their behaviors to be separated.
- F. None of above. chosen
Statements (42)
| Predicate | Object |
|---|---|
| instanceOf |
foundational result of density functional theory
ⓘ
result in quantum mechanics ⓘ theorem ⓘ |
| addresses | many-body problem in quantum mechanics ⓘ |
| appliesTo | systems of interacting electrons in an external potential ⓘ |
| assumes | non-degenerate ground state ⓘ |
| basisOf | density functional theory NERFINISHED ⓘ |
| category |
theorems in mathematical physics
ⓘ
theorems in quantum mechanics ⓘ |
| concerns |
electron density
ⓘ
ground state of quantum systems ⓘ many-electron systems ⓘ |
| contrastWith | wavefunction methods depending on 3N variables for N electrons ⓘ |
| dimensionOfBasicVariable | three-dimensional spatial function ⓘ |
| field |
condensed matter physics
ⓘ
quantum chemistry ⓘ quantum mechanics ⓘ |
| firstTheoremStates | the external potential is a unique functional of the ground-state density ⓘ |
| hasPart |
first Hohenberg–Kohn theorem
NERFINISHED
ⓘ
second Hohenberg–Kohn theorem NERFINISHED ⓘ |
| implies |
existence of a universal energy functional of the electron density
ⓘ
one-to-one correspondence between ground-state density and external potential ⓘ |
| motivates | search for approximate exchange–correlation functionals ⓘ |
| namedAfter |
Pierre Hohenberg
NERFINISHED
ⓘ
Walter Kohn NERFINISHED ⓘ |
| originalAuthors |
Pierre Hohenberg
NERFINISHED
ⓘ
Walter Kohn NERFINISHED ⓘ |
| originalPaperTitle | Inhomogeneous Electron Gas NERFINISHED ⓘ |
| provides | variational principle for the electron density ⓘ |
| publishedIn | Physical Review NERFINISHED ⓘ |
| relatedTo |
Kohn–Sham equations
NERFINISHED
ⓘ
Schrödinger equation NERFINISHED ⓘ variational principle ⓘ |
| replaces | wavefunction as basic variable with electron density ⓘ |
| secondTheoremStates | the correct ground-state density minimizes the energy functional ⓘ |
| states |
all ground-state properties of a many-electron system are functionals of the ground-state electron density
ⓘ
the ground-state electron density uniquely determines the external potential up to an additive constant ⓘ |
| underpins | Kohn–Sham density functional theory NERFINISHED ⓘ |
| usedIn |
computational chemistry
ⓘ
electronic structure calculations ⓘ materials science ⓘ |
| yearProposed | 1964 ⓘ |
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Input
Subject: Hohenberg–Kohn theorem Description of subject: The Hohenberg–Kohn theorem is a foundational result in quantum mechanics that establishes the ground-state electron density as the central quantity determining all properties of a many-electron system, forming the basis of density functional theory.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.