The Hellmann-Feynman Theorem states that once a quantum system's wavefunction has been found for a Hamiltonian depending on some parameter, the derivative of the system's energy with respect to that parameter equals the expectation value of the derivative of the Hamiltonian itself, so that forces and other parameter derivatives can be computed directly from the wavefunction already found rather than by separately differentiating the energy. Named for Hans Hellmann and Richard Feynman, it is a standard computational tool of quantum chemistry and quantum mechanics.
Facts
StatementThe derivative of the total energy with respect to a parameter equals the expectation value of the derivative of the Hamiltonian with respect to that same parameter. 1 Classification
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Entity-backed identity for the statement-form enum value this theorem already carries, resolved to a mathematics concept by an explicit value-to-entity map (phase 3 bucket conversion, docs\design_entity_backed_browse_buckets_20260928.md). The statement-form fact itself stays on the theorem unchanged.
Entity-backed identity for the statement-form enum value this theorem already carries, resolved to a mathematics concept by an explicit value-to-entity map (phase 3 bucket conversion, docs\design_entity_backed_browse_buckets_20260928.md). The statement-form fact itself stays on the theorem unchanged.
Sources
1. Hellmann-Feynman theorem (Wikipedia)
IntroductionQuote, Introduction
the Hellmann-Feynman theorem relates the derivative of the total energy with respect to a parameter to the expectation value of the derivative of the Hamiltonian with respect to that same parameter.
2. Hellmann-Feynman theorem (Wikipedia)
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