Schrödinger equation
E143962
The Schrödinger equation is the fundamental equation of non-relativistic quantum mechanics that governs how the quantum state of a physical system evolves over time.
All labels observed (8)
How this entity was disambiguated
This entity first appeared as the object of triple T1250413 — 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: Schrödinger equation Context triple: [reduced Planck constant, appearsIn, Schrödinger 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.
-
B.
Klein–Gordon equation
The Klein–Gordon equation is a relativistic wave equation that describes spin-0 (scalar) particles in quantum field theory.
-
C.
Pauli equation
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.
-
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.
-
E.
Wheeler–DeWitt equation
The Wheeler–DeWitt equation is a fundamental equation in quantum gravity that attempts to describe the quantum state of the entire universe without reference to time.
- 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: Schrödinger equation Target entity description: The Schrödinger equation is the fundamental equation of non-relativistic quantum mechanics that governs how the quantum state of a physical system evolves over time.
-
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.
Klein–Gordon equation
The Klein–Gordon equation is a relativistic wave equation that describes spin-0 (scalar) particles in quantum field theory.
-
C.
Pauli equation
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.
-
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.
-
E.
Wheeler–DeWitt equation
The Wheeler–DeWitt equation is a fundamental equation in quantum gravity that attempts to describe the quantum state of the entire universe without reference to time.
- F. None of above. chosen
Statements (51)
| Predicate | Object |
|---|---|
| instanceOf |
fundamental equation of quantum mechanics
ⓘ
partial differential equation ⓘ wave equation ⓘ |
| appliesTo | non-relativistic quantum systems ⓘ |
| assumes |
linear dynamics
ⓘ
non-relativistic limit ⓘ |
| contrastWith |
Hamilton–Jacobi equation
ⓘ
surface form:
classical Hamilton–Jacobi equation
|
| describes |
dynamics of wavefunctions
ⓘ
time evolution of quantum states ⓘ |
| domain | Hilbert space ⓘ |
| equivalentTo |
Heisenberg operator formulation of quantum mechanics
ⓘ
surface form:
Heisenberg equation of motion
|
| field | quantum mechanics ⓘ |
| formulatedBy | Erwin Schrödinger ⓘ |
| governs |
evolution of state vectors in Hilbert space
ⓘ
interference phenomena in quantum mechanics ⓘ quantum superposition dynamics ⓘ |
| hasForm |
Schrödinger equation
self-linksurface differs
ⓘ
surface form:
time-dependent Schrödinger equation
Schrödinger equation self-linksurface differs ⓘ
surface form:
time-independent Schrödinger equation
|
| hasOperator |
kinetic energy operator
ⓘ
potential energy operator ⓘ |
| hasSolutionType |
stationary states
ⓘ
wave packets ⓘ |
| implies | continuity equation for probability density ⓘ |
| language |
complex analysis
ⓘ
linear operator theory ⓘ |
| mathematicalForm |
iℏ ∂ψ/∂t = Ĥψ
ⓘ
Ĥψ = Eψ ⓘ |
| property |
conservation of total probability
ⓘ
unitary time evolution ⓘ |
| relatedTo |
Dirac equation
ⓘ
Heisenberg operator formulation of quantum mechanics ⓘ
surface form:
Heisenberg picture
Klein–Gordon equation ⓘ path integral formulation ⓘ |
| requires |
boundary conditions
ⓘ
initial conditions ⓘ |
| underlies |
non-relativistic quantum field theory approximations
ⓘ
quantum chemistry ⓘ |
| usedFor |
atomic spectra calculation
ⓘ
band structure in solids ⓘ hydrogen atom model ⓘ molecular structure calculation ⓘ quantum harmonic oscillator ⓘ quantum scattering theory ⓘ quantum tunneling analysis ⓘ |
| usesConcept |
Hamiltonian operator
ⓘ
Planck constant ⓘ complex-valued wavefunction ⓘ probability amplitude ⓘ wavefunction ⓘ |
| yearProposed | 1925 ⓘ |
| yearPublished | 1926 ⓘ |
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: Schrödinger equation Description of subject: The Schrödinger equation is the fundamental equation of non-relativistic quantum mechanics that governs how the quantum state of a physical system evolves over time.
Referenced by (28)
Full triples — surface form annotated when it differs from this entity's canonical label.
this entity surface form:
many-body Schrödinger equation
this entity surface form:
time-dependent Schrödinger equation
this entity surface form:
Schrödinger equation to relativistic bound states
this entity surface form:
Schrödinger model of the atom
this entity surface form:
Schrödinger equation in absence of spin
this entity surface form:
Schrödinger equation by absence of external time parameter
this entity surface form:
time-dependent Schrödinger equation
this entity surface form:
time-independent Schrödinger equation
this entity surface form:
time-dependent Schrödinger equation
this entity surface form:
time-dependent Schrödinger equation
this entity surface form:
time-independent Schrödinger equation