Pauli equation
E118075
The Pauli equation is a non-relativistic quantum mechanical wave equation that extends the Schrödinger equation to include spin-½ particles interacting with electromagnetic fields.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Pauli equation canonical | 2 |
How this entity was disambiguated
This entity first appeared as the object of triple T1006247 — 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: Pauli equation Context triple: [Dirac equation, nonRelativisticLimit, Pauli equation]
-
A.
Dirac equation
The Dirac equation is a fundamental relativistic wave equation in quantum mechanics that describes spin-½ particles such as electrons and predicts phenomena like antimatter.
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B.
Bethe–Salpeter equation
The Bethe–Salpeter equation is a relativistic quantum field theory equation that describes bound states of two interacting particles, such as electron–hole pairs in quantum electrodynamics.
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C.
Tomonaga–Schwinger equation
The Tomonaga–Schwinger equation is a relativistic generalization of the Schrödinger equation that formulates quantum field evolution on arbitrary spacelike hypersurfaces, forming a key part of covariant quantum field theory.
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D.
Fokker–Planck equation
The Fokker–Planck equation is a partial differential equation that describes the time evolution of the probability density function of a stochastic (random) process, such as Brownian motion.
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E.
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.
- 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: Pauli equation Target entity description: The Pauli equation is a non-relativistic quantum mechanical wave equation that extends the Schrödinger equation to include spin-½ particles interacting with electromagnetic fields.
-
A.
Dirac equation
The Dirac equation is a fundamental relativistic wave equation in quantum mechanics that describes spin-½ particles such as electrons and predicts phenomena like antimatter.
-
B.
Bethe–Salpeter equation
The Bethe–Salpeter equation is a relativistic quantum field theory equation that describes bound states of two interacting particles, such as electron–hole pairs in quantum electrodynamics.
-
C.
Tomonaga–Schwinger equation
The Tomonaga–Schwinger equation is a relativistic generalization of the Schrödinger equation that formulates quantum field evolution on arbitrary spacelike hypersurfaces, forming a key part of covariant quantum field theory.
-
D.
Fokker–Planck equation
The Fokker–Planck equation is a partial differential equation that describes the time evolution of the probability density function of a stochastic (random) process, such as Brownian motion.
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E.
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.
- F. None of above. chosen
Statements (46)
| Predicate | Object |
|---|---|
| instanceOf |
equation in quantum mechanics
ⓘ
non-relativistic equation ⓘ quantum mechanical wave equation ⓘ |
| appliesTo |
electrons
ⓘ
non-relativistic spin-1/2 particles ⓘ |
| assumes |
Galilean invariance
ⓘ
non-relativistic velocities ⓘ |
| contains |
kinetic energy operator with covariant derivative
ⓘ
magnetic field term proportional to sigma dot B ⓘ |
| derivedFrom | Dirac equation in the non-relativistic limit ⓘ |
| describes |
dynamics of spin in electromagnetic fields
ⓘ
magnetic moment of electron ⓘ spin-1/2 particles ⓘ |
| domain |
atomic physics
ⓘ
condensed matter physics ⓘ quantum theory of spin ⓘ |
| extends | Schrödinger equation ⓘ |
| fieldType | two-component complex field ⓘ |
| formalism | spinor formalism ⓘ |
| framework | non-relativistic quantum mechanics ⓘ |
| governs | time evolution of spinor wavefunctions ⓘ |
| historicalPeriod | 20th century physics ⓘ |
| includes |
Pauli matrices
ⓘ
surface form:
Pauli spin matrices
Zeeman interaction term ⓘ magnetic moment interaction ⓘ minimal coupling to electromagnetic potentials ⓘ scalar potential of electromagnetic field ⓘ spin interaction with electromagnetic fields ⓘ spin-orbit coupling in appropriate limits ⓘ vector potential of electromagnetic field ⓘ |
| mathematicalForm |
first-order in time
ⓘ
second-order in spatial derivatives ⓘ |
| namedAfter | Wolfgang Pauli ⓘ |
| predicts | spin precession in magnetic fields ⓘ |
| reducesTo |
Schrödinger equation
ⓘ
surface form:
Schrödinger equation in absence of spin
Schrödinger equation when magnetic field is zero ⓘ |
| relatedConcept |
Pauli spin matrices
ⓘ
Zeeman effect ⓘ spin magnetic moment ⓘ spin-orbit interaction ⓘ |
| relatedTo | Dirac equation ⓘ |
| usedFor |
Landau level calculations in non-relativistic limit
ⓘ
description of fine structure in atoms ⓘ modeling electrons in magnetic materials ⓘ |
| uses |
Pauli matrices
ⓘ
two-component spinor wavefunctions ⓘ |
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.
Instruction
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.
Input
Subject: Pauli equation Description of subject: The Pauli equation is a non-relativistic quantum mechanical wave equation that extends the Schrödinger equation to include spin-½ particles interacting with electromagnetic fields.
Referenced by (2)
Full triples — surface form annotated when it differs from this entity's canonical label.