Sommerfeld radiation condition
E234762
The Sommerfeld radiation condition is a mathematical criterion in wave and scattering theory that selects physically meaningful, outward-radiating solutions to the Helmholtz equation at infinity.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Sommerfeld radiation condition canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T2093724 — 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: Sommerfeld radiation condition Context triple: [Arnold Sommerfeld, knownFor, Sommerfeld radiation condition]
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A.
Kirchhoff diffraction theory
Kirchhoff diffraction theory is a classical wave optics framework that models light propagation and diffraction by treating wavefronts as superpositions of secondary spherical waves emitted from an aperture.
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B.
Hertzian waves
Hertzian waves are early experimentally demonstrated electromagnetic waves that confirmed James Clerk Maxwell’s theory of electromagnetism and paved the way for modern radio communication.
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C.
Huygens–Fresnel principle
The Huygens–Fresnel principle is a fundamental concept in wave optics that explains how every point on a wavefront acts as a source of secondary wavelets whose interference determines the wave’s subsequent propagation and diffraction.
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D.
Fresnel equations
The Fresnel equations are fundamental formulas in optics that describe how light is partially reflected and transmitted at the boundary between two media with different refractive indices, depending on polarization and angle of incidence.
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E.
Condon–Shortley phase
The Condon–Shortley phase is a sign convention introduced in quantum mechanics to standardize the definition of spherical harmonics and angular momentum coupling coefficients.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
Target entity: Sommerfeld radiation condition Target entity description: The Sommerfeld radiation condition is a mathematical criterion in wave and scattering theory that selects physically meaningful, outward-radiating solutions to the Helmholtz equation at infinity.
-
A.
Kirchhoff diffraction theory
Kirchhoff diffraction theory is a classical wave optics framework that models light propagation and diffraction by treating wavefronts as superpositions of secondary spherical waves emitted from an aperture.
-
B.
Hertzian waves
Hertzian waves are early experimentally demonstrated electromagnetic waves that confirmed James Clerk Maxwell’s theory of electromagnetism and paved the way for modern radio communication.
-
C.
Huygens–Fresnel principle
The Huygens–Fresnel principle is a fundamental concept in wave optics that explains how every point on a wavefront acts as a source of secondary wavelets whose interference determines the wave’s subsequent propagation and diffraction.
-
D.
Fresnel equations
The Fresnel equations are fundamental formulas in optics that describe how light is partially reflected and transmitted at the boundary between two media with different refractive indices, depending on polarization and angle of incidence.
-
E.
Condon–Shortley phase
The Condon–Shortley phase is a sign convention introduced in quantum mechanics to standardize the definition of spherical harmonics and angular momentum coupling coefficients.
- F. None of above. chosen
Statements (51)
| Predicate | Object |
|---|---|
| instanceOf |
boundary condition
ⓘ
concept in scattering theory ⓘ concept in wave theory ⓘ mathematical condition ⓘ radiation condition ⓘ |
| appliesTo |
Helmholtz equation
ⓘ
acoustic waves ⓘ electromagnetic waves ⓘ scalar wave equation in frequency domain ⓘ scattering problems ⓘ time-harmonic wave fields ⓘ |
| assumes | time dependence e^{-iωt} ⓘ |
| characterizes | outgoing waves at infinity ⓘ |
| contrastsWith |
Dirichlet boundary conditions
ⓘ
surface form:
Dirichlet boundary condition at finite distance
Neumann boundary conditions in potential theory ⓘ
surface form:
Neumann boundary condition at finite distance
incoming radiation condition ⓘ periodic boundary conditions ⓘ |
| domain |
mathematical physics
ⓘ
partial differential equations ⓘ scattering theory ⓘ wave propagation ⓘ |
| ensures |
causal radiation behavior in frequency domain
ⓘ
finite energy flux at infinity ⓘ uniqueness of the scattered field ⓘ |
| generalizationOf | radiation conditions for other elliptic operators ⓘ |
| hasConsequence |
existence of far-field pattern
ⓘ
representation of solutions via asymptotic expansions ⓘ well-posedness of exterior scattering problems ⓘ |
| imposes | asymptotic behavior on wave fields ⓘ |
| mathematicalForm |
lim_{r→∞} r(∂u/∂r - iku) = 0 in three dimensions
ⓘ
lim_{r→∞} r^{(d-1)/2}(∂u/∂r - iku) = 0 for d-dimensional space ⓘ |
| namedAfter | Arnold Sommerfeld ⓘ |
| purpose |
to enforce outward-radiating behavior at infinity
ⓘ
to ensure uniqueness of solutions to exterior boundary value problems ⓘ to exclude incoming waves from infinity ⓘ to select physically meaningful solutions of the Helmholtz equation ⓘ |
| relatedTo |
Lippmann–Schwinger equation
ⓘ
limiting absorption principle ⓘ outgoing Green's function of the Helmholtz operator ⓘ |
| relatesTo |
far-field behavior of solutions
ⓘ
radiation of energy to infinity ⓘ |
| timePeriod | early 20th century ⓘ |
| usedBy |
applied mathematicians
ⓘ
engineers ⓘ physicists ⓘ |
| usedIn |
acoustic scattering by obstacles
ⓘ
antenna theory ⓘ electromagnetic scattering by conductors ⓘ exterior Dirichlet problems ⓘ exterior Neumann problems ⓘ seismology wave propagation models ⓘ |
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: Sommerfeld radiation condition Description of subject: The Sommerfeld radiation condition is a mathematical criterion in wave and scattering theory that selects physically meaningful, outward-radiating solutions to the Helmholtz equation at infinity.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.