The Adiabatic Theorem of quantum mechanics states that a physical system starting in an eigenstate of a slowly and continuously varying Hamiltonian will remain, at each later time, in the corresponding instantaneous eigenstate of that Hamiltonian, provided the variation is slow enough relative to the gaps between the system's energy levels. First stated by Max Born and Vladimir Fock, it justifies the widespread practice of tracking a quantum state by tracking the eigenstate it began in, and underlies techniques such as adiabatic quantum computation.
Facts
StatementA quantum mechanical system subjected to gradually changing external conditions adapts its functional form to the changing conditions, while a system subjected to rapidly varying conditions has no time to adapt, so its spatial probability density remains unchanged. 1 Classification
Statement FormCharacterization Theorem 1 Connections
Has Statement Form
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. Adiabatic Theorem (Wikipedia)
Wikimedia Foundationopening paragraphQuote, opening paragraph
Its original form, due to Max Born and Vladimir Fock (1928), was stated as follows:
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