Bloch waves
E166546
Bloch waves are quantum-mechanical wavefunctions that describe particles, such as electrons, propagating through a periodic crystal lattice and form the basis for understanding electronic band structure in solids.
All labels observed (4)
| Label | Occurrences |
|---|---|
| Bloch theorem | 2 |
| Bloch waves canonical | 1 |
| Bloch's theorem | 1 |
| Wannier functions | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T1455590 — 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: Bloch waves Context triple: [Felix Bloch, notableWork, Bloch waves]
-
A.
Brillouin zone
The Brillouin zone is the fundamental region of reciprocal space in a crystal lattice, defining the allowed wavevectors for electrons and underpinning the structure of electronic band diagrams.
-
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.
Anderson localization
Anderson localization is a quantum mechanical phenomenon in which disorder in a material causes electrons or waves to become spatially localized, preventing them from diffusing freely.
-
D.
Peierls substitution
Peierls substitution is a quantum mechanical method for incorporating the effects of an external electromagnetic field into the momentum of charged particles in lattice or solid-state systems.
-
E.
Quantum Theory of Solids
Quantum Theory of Solids is a foundational physics text that systematically applies quantum mechanics to explain the electronic, thermal, and structural properties of crystalline solids.
- 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: Bloch waves Target entity description: Bloch waves are quantum-mechanical wavefunctions that describe particles, such as electrons, propagating through a periodic crystal lattice and form the basis for understanding electronic band structure in solids.
-
A.
Brillouin zone
The Brillouin zone is the fundamental region of reciprocal space in a crystal lattice, defining the allowed wavevectors for electrons and underpinning the structure of electronic band diagrams.
-
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.
Anderson localization
Anderson localization is a quantum mechanical phenomenon in which disorder in a material causes electrons or waves to become spatially localized, preventing them from diffusing freely.
-
D.
Peierls substitution
Peierls substitution is a quantum mechanical method for incorporating the effects of an external electromagnetic field into the momentum of charged particles in lattice or solid-state systems.
-
E.
Quantum Theory of Solids
Quantum Theory of Solids is a foundational physics text that systematically applies quantum mechanics to explain the electronic, thermal, and structural properties of crystalline solids.
- F. None of above. chosen
Statements (47)
| Predicate | Object |
|---|---|
| instanceOf |
concept in solid-state physics
ⓘ
quantum-mechanical wavefunction ⓘ solution of Schrödinger equation ⓘ |
| appliesTo |
electrons in solids
ⓘ
periodic crystal lattices ⓘ phonons in crystals ⓘ photons in photonic crystals ⓘ |
| basedOn |
Bloch waves
self-linksurface differs
ⓘ
surface form:
Bloch theorem
|
| contrastedWith | localized atomic orbitals ⓘ |
| definedIn | Hilbert space of crystal states ⓘ |
| describes |
electrons in a crystal lattice
ⓘ
particles in a periodic potential ⓘ |
| domain |
condensed matter physics
ⓘ
quantum mechanics ⓘ solid-state physics ⓘ |
| emergesFrom | discrete translational invariance ⓘ |
| generalizationOf | plane waves in free space ⓘ |
| hasConsequence |
electron delocalization in crystals
ⓘ
formation of allowed and forbidden energy bands ⓘ |
| hasMathematicalForm | ψ_k(r) = e^{i k·r} u_k(r) ⓘ |
| hasParameter |
band index n
ⓘ
wave vector k ⓘ |
| hasProperty |
characterized by crystal momentum k
ⓘ
extend over the entire crystal ⓘ reflect discrete translational symmetry ⓘ u_k(r) has lattice periodicity ⓘ |
| namedAfter | Felix Bloch ⓘ |
| relatedTo |
Bloch states
ⓘ
Brillouin zone ⓘ Bloch waves self-linksurface differs ⓘ
surface form:
Wannier functions
band structure ⓘ crystal momentum ⓘ energy bands ⓘ periodic boundary conditions ⓘ reciprocal lattice ⓘ |
| satisfies | Bloch periodic boundary conditions ⓘ |
| usedFor |
deriving electronic band structure
ⓘ
explaining band gaps ⓘ explaining energy bands in solids ⓘ nearly-free electron model ⓘ solid-state spectroscopy analysis ⓘ tight-binding calculations ⓘ |
| usedIn |
phonon dispersion calculations
ⓘ
photonic band theory ⓘ semiconductor physics ⓘ theory of electrical conductivity ⓘ theory of metals ⓘ |
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: Bloch waves Description of subject: Bloch waves are quantum-mechanical wavefunctions that describe particles, such as electrons, propagating through a periodic crystal lattice and form the basis for understanding electronic band structure in solids.
Referenced by (5)
Full triples — surface form annotated when it differs from this entity's canonical label.
this entity surface form:
Bloch theorem
this entity surface form:
Bloch's theorem
this entity surface form:
Bloch theorem
this entity surface form:
Wannier functions