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Landau–Zener formula — Wikipedia (en)

Source: Wikipedia (en)
Original: https://en.wikipedia.org/wiki/Landau%E2%80%93Zener_formula
License (as archived): CC-BY-SA-4.0
Archived: 2026-10-07T15:39:48.735Z
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Landau–Zener formula — Wikipedia (en) — Wikipedia (en), https://en.wikipedia.org/wiki/Landau%E2%80%93Zener_formula (CC-BY-SA-4.0); archived copy: https://metraipolis.com/documento/dc_33d58331e245 (Metraipolis archive dc_33d58331e245, sha256 65e697c9b57e24a3603df23dff0f4e08b1021ed5cc6e1ff566a918276974af47)

BibTeX

@misc{dc33d58331e245,
  title = {Landau–Zener formula — Wikipedia (en)},
  howpublished = {Wikipedia (en)},
  url = {https://en.wikipedia.org/wiki/Landau%E2%80%93Zener_formula},
  note = {License CC-BY-SA-4.0; archived copy https://metraipolis.com/documento/dc_33d58331e245; sha256 65e697c9b57e24a3603df23dff0f4e08b1021ed5cc6e1ff566a918276974af47},
  year = {2026}
}

Archived text

Reproduced under CC-BY-SA-4.0. Attribution: Wikipedia (en), https://en.wikipedia.org/wiki/Landau%E2%80%93Zener_formula. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

The Landau–Zener formula is an analytic solution to the equations of motion governing the transition dynamics of a two-state quantum system, with a time-dependent semi-classical Hamiltonian varying such that the energy separation of the two states is a linear function of time. The formula, giving the probability of a non-adiabatic transition between the two adiabatic energy states, was published separately by Lev Landau, Clarence Zener, Ernst Stueckelberg, and Ettore Majorana, in 1932. If the system starts, in the infinite past, in the lower energy eigenstate, we wish to calculate the probability of finding the system in the upper energy eigenstate in the infinite future (a so-called Landau–Zener transition). For infinitely slow variation of the energy difference (that is, a Landau–Zener velocity of zero), the adiabatic theorem tells us that no such transition will take place in absence of any external fields, as the system will always be in an instantaneous eigenstate of the Hamiltonian at every moment of time. At non-zero velocities, non-adiabatic transitions can occur with a probability approximated by the Landau–Zener formula.

Tema degli esploratori: fisica e astronomia (deposito sistematico; categoria «Quantum mechanics»).
Fonte: Wikipedia in inglese, voce «Landau–Zener formula» — https://en.wikipedia.org/wiki/Landau%E2%80%93Zener_formula
Wikidata Q3025195 (dati Wikidata in CC0 1.0) — https://www.wikidata.org/wiki/Q3025195
Autori: i contributori di Wikipedia (cronologia: https://en.wikipedia.org/wiki/Landau%E2%80%93Zener_formula?action=history).
Licenza: Creative Commons Attribuzione-Condividi allo stesso modo 4.0 (CC BY-SA 4.0) — https://creativecommons.org/licenses/by-sa/4.0/. Il riuso richiede attribuzione e stessa licenza.
Estratto dell'introduzione non modificato nel contenuto; revisione 1362851780, consultata il 2026-10-07T15:11:59.479Z tramite l'API ufficiale di Wikipedia. Impronta SHA-256 dell'estratto: 5fad089340d3eeb14ca28764d4c81a5bd62bc143b602b06a44283ce962ed7867