Landau–Zener formula
E334543
The Landau–Zener formula is a quantum mechanical result that gives the probability of non-adiabatic transitions between energy levels during an avoided crossing when a system’s parameters are varied in time.
All labels observed (4)
| Label | Occurrences |
|---|---|
| Landau–Zener formula canonical | 1 |
| Landau–Zener model | 1 |
| Landau–Zener transition formula | 1 |
| Landau–Zener–Stückelberg–Majorana theory | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T3175507 — 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.
Target entity: Landau–Zener formula Context triple: [Lev Landau, knownFor, Landau–Zener formula]
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A.
Herzberg–Teller approximation
The Herzberg–Teller approximation is a refinement in molecular spectroscopy that accounts for vibronic coupling by allowing electronic transition dipole moments to depend on nuclear coordinates, explaining intensity in otherwise forbidden transitions.
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B.
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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C.
Rabi oscillation
Rabi oscillation is a quantum mechanical phenomenon in which a two-level system, such as an atom or qubit, undergoes coherent periodic transitions between its states when driven by a resonant oscillatory field.
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D.
Rayleigh–Schrödinger perturbation theory
Rayleigh–Schrödinger perturbation theory is a fundamental method in quantum mechanics for approximating the energies and states of a system by treating interactions as small corrections to an exactly solvable problem.
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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.
Target entity: Landau–Zener formula Target entity description: The Landau–Zener formula is a quantum mechanical result that gives the probability of non-adiabatic transitions between energy levels during an avoided crossing when a system’s parameters are varied in time.
-
A.
Herzberg–Teller approximation
The Herzberg–Teller approximation is a refinement in molecular spectroscopy that accounts for vibronic coupling by allowing electronic transition dipole moments to depend on nuclear coordinates, explaining intensity in otherwise forbidden transitions.
-
B.
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.
-
C.
Rabi oscillation
Rabi oscillation is a quantum mechanical phenomenon in which a two-level system, such as an atom or qubit, undergoes coherent periodic transitions between its states when driven by a resonant oscillatory field.
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D.
Rayleigh–Schrödinger perturbation theory
Rayleigh–Schrödinger perturbation theory is a fundamental method in quantum mechanics for approximating the energies and states of a system by treating interactions as small corrections to an exactly solvable problem.
-
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 (48)
| Predicate | Object |
|---|---|
| instanceOf |
physical law
ⓘ
quantum mechanical formula ⓘ result in quantum mechanics ⓘ |
| alsoKnownAs |
Landau–Zener formula
ⓘ
surface form:
Landau–Zener model
Landau–Zener formula ⓘ
surface form:
Landau–Zener transition formula
|
| appliesTo |
avoided level crossings
ⓘ
time-dependent Hamiltonians ⓘ two-level quantum systems ⓘ |
| assumes |
constant coupling between two levels
ⓘ
linearly time-dependent energy bias between diabatic states ⓘ two-level approximation ⓘ |
| context |
adiabatic theorem in quantum mechanics
ⓘ
Schrödinger equation ⓘ
surface form:
time-dependent Schrödinger equation
|
| dependsOn |
Planck constant
ⓘ
rate of change of the energy level separation ⓘ square of the coupling matrix element ⓘ |
| describes |
non-adiabatic transitions between energy levels
ⓘ
transition probability at an avoided level crossing ⓘ |
| field |
atomic physics
ⓘ
condensed matter physics ⓘ molecular physics ⓘ quantum mechanics ⓘ quantum optics ⓘ |
| gives |
probability of adiabatic transition between eigenstates
ⓘ
probability of diabatic transition ⓘ probability of remaining in the initial diabatic state ⓘ |
| influenced |
design of Landau–Zener sweeps in qubit control
ⓘ
development of adiabatic quantum computation ⓘ |
| mathematicalForm | transition probability expressed as an exponential of a non-adiabatic parameter ⓘ |
| namedAfter |
Clarence Zener
ⓘ
Lev Landau ⓘ |
| relatedTo |
Landau–Zener formula
self-linksurface differs
ⓘ
surface form:
Landau–Zener–Stückelberg–Majorana theory
Rabi oscillation ⓘ
surface form:
Rabi oscillations
Stückelberg interferometry ⓘ adiabatic approximation ⓘ diabatic basis ⓘ |
| testedIn |
molecular collision experiments
ⓘ
semiconductor quantum dots ⓘ superconducting qubits ⓘ ultracold atoms in optical lattices ⓘ |
| usedFor |
analyzing quantum tunneling in energy level crossings
ⓘ
characterizing decoherence in qubits ⓘ designing adiabatic quantum control protocols ⓘ estimating transition probabilities in driven quantum systems ⓘ spectroscopy of avoided crossings ⓘ |
| validWhen |
sweep through avoided crossing is approximately linear in time
ⓘ
system is isolated from strong environmental decoherence ⓘ |
| yearProposed | 1932 ⓘ |
How these facts were elicited
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Subject: Landau–Zener formula Description of subject: The Landau–Zener formula is a quantum mechanical result that gives the probability of non-adiabatic transitions between energy levels during an avoided crossing when a system’s parameters are varied in time.
Referenced by (4)
Full triples — surface form annotated when it differs from this entity's canonical label.