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Fundamental theorem in condensed matter physics
In condensed matter physics, Bloch's theorem states that solutions to the Schrödinger equation in a periodic potential can be expressed as plane waves
Bloch's_theorem
Mathematical theorem
In complex analysis, a branch of mathematics, Bloch's theorem describes the behaviour of holomorphic functions defined on the unit disk. It gives a lower
Bloch's theorem (complex analysis)
Bloch's_theorem_(complex_analysis)
Theorem relating Milnor K-theory and Galois cohomology
In mathematics, the norm residue isomorphism theorem is a long-sought result relating Milnor K-theory and Galois cohomology. The result has a relatively
Norm residue isomorphism theorem
Norm_residue_isomorphism_theorem
principle, Picard's theorem corresponds to Schottky's theorem, and Valiron's theorem corresponds to Bloch's theorem. Based on his Principle, Bloch was able to
Bloch's_principle
Branch of ordinary differential equations
such as crystals in condensed matter physics, the result is known as Bloch's theorem. Note that the solutions of the linear differential equation form a
Floquet_theory
French mathematician (1893–1948)
Picard's theorem.) His proof of this theorem contained gaps (which he recognized), and later the theorem was known as "Bloch's conjecture". Bloch's conjecture
André_Bloch_(mathematician)
Describes the range of energies of an electron within the solid
special case of electron waves in a periodic crystal lattice using Bloch's theorem as treated generally in the dynamical theory of diffraction. Every
Electronic_band_structure
Solid-state physics model
periodic function, with the same periodicity as the crystal lattice. Bloch's theorem proves that the solutions to this differential equation can be written
K·p_perturbation_theory
Physics software package
coordinates (the Born–Oppenheimer approximation). The code also makes use of Bloch's Theorem which means a wavefunction of a periodic system has a cell-periodic
CASTEP
Concept in physics
periodicity of the crystalline potential allows the application of the Bloch theorem, which states that the Hamiltonian eigenstates take the form ψ n k (
Berry connection and curvature
Berry_connection_and_curvature
Quantum-mechanical vector property in solid-state physics
associated conservation law cannot be derived using Noether's theorem. The phase modulation of the Bloch state ψ n ( x ) = e i k ⋅ x u n k ( x ) {\displaystyle
Crystal_momentum
Operator shifting particles and fields by a certain amount in a certain direction
{k} \cdot \mathbf {R} }\psi (\mathbf {r} )} This result is known as Bloch's Theorem. In the passive transformation picture, translational invariance requires
Translation operator (quantum mechanics)
Translation_operator_(quantum_mechanics)
Model in Quantum Physics
the potential is a periodic function with a period a. According to Bloch's theorem, the wavefunction solution of the Schrödinger equation when the potential
Particle in a one-dimensional lattice
Particle_in_a_one-dimensional_lattice
Periodic boundary condition in solid-state physics
condition and plugging in Schrödinger's equation results in a proof of Bloch's theorem, which is particularly important in understanding the band structure
Born–von Karman boundary condition
Born–von_Karman_boundary_condition
Swiss-American physicist (1905–1983)
Felix Bloch (23 October 1905 – 10 September 1983) was a Swiss–American theoretical physicist who shared the 1952 Nobel Prize in Physics with Edward Mills
Felix_Bloch
Primitive cell in the reciprocal space lattice of crystals
stems from the description of waves in a periodic medium given by Bloch's theorem, in which it is found that the solutions can be completely characterized
Brillouin_zone
Branch of physics focused on matter in the solid state
periodic potential. The solutions in this case are known as Bloch states. Since Bloch's theorem applies only to periodic potentials, and since unceasing
Solid-state_physics
Model of electronic band structures of solids
a solid need not be carried out with full rigor as in the original Bloch's theorem but, rather, first-principles calculations are carried out only at
Tight_binding
Class of functions behaving "like" periodic functions
quasiperiods, the periods of the corresponding Weierstrass ℘ function. Bloch's theorem says that the eigenfunctions of a periodic Schrödinger equation (or
Quasiperiodic_function
Topics referred to by the same term
potential; see Bloch's theorem. Named after French mathematician André Bloch an analytic function in the unit disc which is an element of the Bloch space. This
Bloch_function
theorem (logic) Diaconescu's theorem (mathematical logic) Easton's theorem (set theory) Erdős–Dushnik–Miller theorem (set theory) Erdős–Rado theorem (set
List_of_theorems
Canadian mathematician
by Maciejko and Rayan, Automorphic Bloch theorems for hyperbolic lattices, developed a generalized Bloch theorem for finite hyperbolic lattices. That
Steven_Rayan
Model of electrons within a metallic solid
electron models came in 1928, with Felix Bloch dissertation, under the supervision of Werner Heisenberg. Bloch's theorem introduced the electron wave behavior
Free_electron_model
Parody of the laws of thermodynamics
Ginsberg's theorem is an epigrammatic paraphrase and parody "theorem" which restates or analogizes the consequences of the four laws of thermodynamics
Ginsberg's_theorem
Function with a repeating pattern
necessarily true. A further generalization appears in the context of Bloch's theorems and Floquet theory, which govern the solution of various periodic differential
Periodic_function
Physical model of solid metals as electron gases
independent electron approximation is still in effect. As shown by Bloch's theorem, introducing a periodic potential into the Schrödinger equation results
Nearly_free_electron_model
Scientific field of study
physics, Nanoscale and mesoscopic physics, Polymer physics BCS theory, Bloch's theorem, Density functional theory, Fermi gas, Fermi liquid theory, Many-body
Physics
Metal with a small negative indirect band-gap
against the crystal momentum of conduction electrons. According to the Bloch theorem the conduction of electrons depends on the periodicity of the crystal
Semimetal
Theorem in quantum mechanics
analogous result for quantum electrodynamics alone is known as Bloch–Nordsieck theorem. Ultraviolet divergences in perturbative quantum field theory are
Kinoshita–Lee–Nauenberg theorem
Kinoshita–Lee–Nauenberg_theorem
Route Bloch, at CERN (Meyrin site) Bloch Auditorium, Hewlett Teaching Center room 201, Stanford University Bloch Beamline at MAX IV Laboratory Bloch Fellowship
List of things named after Felix Bloch
List_of_things_named_after_Felix_Bloch
Extended physical object in string theory
physics, Nanoscale and mesoscopic physics, Polymer physics BCS theory, Bloch's theorem, Density functional theory, Fermi gas, Fermi liquid theory, Many-body
Brane
Electronic states at the surface of materials
stated by Bloch's theorem, eigenstates of the single-electron Schrödinger equation with a perfectly periodic potential, a crystal, are Bloch waves Ψ n
Surface_states
Light wave refraction with opposite properties to those usually observed
crystal Seismic metamaterials Split-ring resonator Tunable metamaterials Bloch's theorem Casimir effect Dielectric Electromagnetism EM radiation Electron mobility
Negative_refraction
Description of a quantum-mechanical system
Schrödinger equation is often written for functions of momentum, as Bloch's theorem ensures the periodic crystal lattice potential couples Ψ ~ ( p ) {\displaystyle
Schrödinger_equation
Simplified model in condensed matter physics
which the effect had first been observed. Anderson impurity model Bloch's theorem Electronic band structure Solid-state physics Bose–Hubbard model t-J
Hubbard_model
Vector describing a wave; often its propagation direction
via that envelope wave, usually using the "physics definition". See Bloch's theorem for further details. A moving wave surface in special relativity may
Wave_vector
Conceptual opposite of an electron
pioneered in 1929 by Rudolf Peierls, who analyzed the Hall effect using Bloch's theorem, and demonstrated that a nearly full and a nearly empty Brillouin zones
Electron_hole
List of terms created from a person's name
André Bloch, French mathematician, Bloch space, Bloch's theorem (complex variables) Felix Bloch, Swiss-American physician – Bloch wall, Bloch sphere
List_of_eponyms_(A–K)
Classic textbook in by Charles Kittel
book covers a wide range of topics in solid state physics, including Bloch's theorem, crystals, magnetism, phonons, Fermi gases, magnetic resonance, and
Introduction to Solid State Physics
Introduction_to_Solid_State_Physics
Theorem in quantum mechanics
In mathematical physics, Gleason's theorem shows that the rule one uses to calculate probabilities in quantum physics, the Born rule, can be derived from
Gleason's_theorem
Anomalous diffraction at metallic gratings
A rigorous theory of Wood anomalies can be developed by invoking Bloch's theorem and expanding electromagnetic fields as spatial harmonics, whose boundary
Wood's_anomaly
State of matter with insulating bulk but conductive boundary
+b|B\rangle } (where A and B are the internal degrees of freedom). Due to Bloch's theorem, this basis block-diagonalizes the Hamiltonian. One such block, h k
Topological_insulator
Representation of a quantum mechanical system
In quantum mechanics and computing, the Bloch sphere is a geometrical representation of the pure state space of a two-level quantum mechanical system
Bloch_sphere
Overview of and topical guide to physics
physics, nanoscale and mesoscopic physics, polymer physics BCS theory, Bloch's theorem, Fermi gas, Fermi liquid, many-body theory Phases (gas, liquid, solid
Outline_of_physics
Bandwidth-limited pulse beat Berry phase Bessel beam Beta wave Black hole Blazar Bloch's theorem Blueshift Boussinesq approximation (water waves) Bow wave Bragg diffraction
Index_of_wave_articles
Number with an integer power equal to 1
that also follows from group representation theory as a variant of Bloch's theorem.[page needed] In particular, if a circulant Hermitian matrix is considered
Root_of_unity
Physical function
topological materials WannierBerri - a python code for Wannier interpolation and tight-binding calculations Bloch's theorem Hannay angle Geometric phase
Wannier_function
Dynamic disturbance in a medium or field
for a tsunami Tollmien–Schlichting wave, in fluid dynamics Wind wave Bloch's theorem Matter wave Pilot wave theory, in Bohmian mechanics Wave function Wave
Wave
Simplification that approximates the electron–electron interaction in crystals as null
model and the nearly-free electron model, where it is used alongside Bloch's theorem. In quantum mechanics, this approximation is often used to simplify
Independent electron approximation
Independent_electron_approximation
Theory for waves passing through multiple obstacles
periodic array. Bloch's theorem holds for such a system, which means that the solutions of the Schrödinger equation may be written as a Bloch wave ψ k ( r
Multiple_scattering_theory
Two theorems about families of holomorphic functions
In complex analysis, an area of mathematics, Montel's theorem refers to one of two theorems about families of holomorphic functions. These are named after
Montel's_theorem
Non-periodic tiling of the plane
properties, such as electronic structure, difficult due to the absence of Bloch's theorem. However, spectra of quasicrystals can still be computed with error
Penrose_tiling
Software package for electron configuration calculations EXCITING Bloch's theorem Project augmented wave, www.wfu.edu, undated (accessed 21 January 2007)
Pwpaw
Mathematical model in quantum mechanics
wavelengths, and higher resistance to light than other substances. Bloch's theorem Configuration integral (statistical mechanics) Delta function potential
Particle_in_a_box
Experimental technique to determine the distribution of electrons in solids
according to Bloch's theorem. From the plane-wave factor exp ( i k ⋅ r ) {\displaystyle \exp(i\mathbf {k} \cdot \mathbf {r} )} in Bloch's decomposition
Angle-resolved photoemission spectroscopy
Angle-resolved_photoemission_spectroscopy
further simplified with the use of group theory and in particular Bloch's theorem, which leads to the result that the energy eigenvalues depend on the
Korringa–Kohn–Rostoker_method
Yang–Mills theory vacuum state
the form that eigenstates take in periodic potentials according to Bloch's theorem, the vacuum state is a coherent sum of topological vacua | θ ⟩ = ∑
Theta_vacuum
hu. Retrieved 2026-07-20. Hraskó, András (December 2002). "Poncelet's theorem". Mathematical and Physical Journal for Secondary Schools. 1 (1). ISSN 1215-9247
List of mathematicians who did research in prison
List_of_mathematicians_who_did_research_in_prison
Quasiparticle which is a bound state of an electron and an electron hole
composite particle in the crystalline lattice in agreement with the Bloch theorem. The exciton energy depends on K and is typically parabolic for the
Exciton
Branch of physics
physicist Felix Bloch provided a wave function solution to the Schrödinger equation with a periodic potential, known as Bloch's theorem. Calculating electronic
Condensed_matter_physics
Ordered chemical structure with no repeating pattern
While crystals, according to the classical crystallographic restriction theorem, can possess only two-, three-, four-, and six-fold rotational symmetries
Quasicrystal
Material designed to manipulate sound waves
material. To obtain the frequency band structure of a phononic crystal, Bloch's theorem is applied on a single unit cell in the reciprocal lattice space (Brillouin
Acoustic_metamaterial
Periodic structure of layers of two or more materials
2\pi /d} with over d = a + b {\displaystyle d=a+b} by virtue of the Bloch theorem, is fully sinusoidal: E z ( k z ) = Δ 2 ( 1 − cos ( k z d ) ) {\displaystyle
Superlattice
Electronic structure method
\right)} is the potential landscape due to the crystal lattice. The Bloch theorem asserts that the solution to the problem: H Ψ k ( r ) = E ( k ) Ψ k
Peierls_substitution
Fourier transform of a real-space lattice, important in solid-state physics
lattice, which plays an important role in solid state physics due to Bloch's theorem. In pure mathematics, the dual space of linear forms and the dual lattice
Reciprocal_lattice
Curves of genus > 1 over the rationals have only finitely many rational points
Faltings' theorem is a result in arithmetic geometry, according to which a non-singular algebraic curve of genus greater than 1 over the field Q {\displaystyle
Faltings'_theorem
introduce the concept of molecular orbitals. 1929: Felix Bloch demonstrates Bloch's theorem. John Lennard-Jones introduces the linear combination of atomic
Timeline of condensed matter physics
Timeline_of_condensed_matter_physics
Dutch-American physicist (1915–2015)
to calculate the electronic states of non-periodic solids for which Bloch’s theorem does not hold. In 1958 he published an approach, now called the average
Jan_Korringa
No spontaneous symmetry breaking in two-dimensional systems at finite temperature
Hohenberg–Mermin–Wagner theorem or Mermin–Wagner theorem (also known as Mermin–Wagner–Berezinskii theorem or Mermin–Wagner–Coleman theorem) states that continuous
Mermin–Wagner_theorem
spin spirals with deviating periodicity is based on the generalized Bloch theorem. The code offers native support for the description of three-dimensional
FLEUR
Paradigmatic model
= l ℏ {\displaystyle p=l\hbar } , l {\displaystyle l} integer) see Bloch theorem), so that ⟨ θ | ψ ⟩ = ∑ l = − ∞ ∞ ⟨ l | ψ ⟩ e i l θ ⇔ ⟨ l | ψ ⟩ = ∫
Kicked_rotator
Mathematical theory
defined. A quantitative version of this statement is known as the Bloch theorem. This theorem of Valiron has further applications in holomorphic dynamics:
Wiman–Valiron_theory
Theorem in the mathematical formulation of quantum mechanics
Wigner's theorem, proved by Eugene Wigner in 1931, is a cornerstone of the mathematical formulation of quantum mechanics. The theorem specifies how physical
Wigner's_theorem
introduced by Spencer Bloch (Bloch 1986) and the basic theory has been developed by Bloch and Marc Levine. In more precise terms, a theorem of Voevodsky implies:
Bloch's_higher_Chow_group
Statement in complex analysis
theorem provides a related estimate in the case that f {\displaystyle f} is univalent. Nevanlinna–Pick interpolation Kobayashi hyperbolicity Bloch's principle
Schwarz_lemma
The Lyapunov–Malkin theorem (named for Aleksandr Lyapunov and Ioel Malkin [ru]) is a mathematical theorem detailing stability of nonlinear systems. In
Lyapunov–Malkin_theorem
Theorem stating the impossibility of converting qubits into bits
In quantum information theory, the no-teleportation theorem states that an arbitrary quantum state cannot be converted into a sequence of classical bits
No-teleportation_theorem
Algebraic theorem
In algebra, the Milnor–Moore theorem, introduced by John W. Milnor and John C. Moore (1965) classifies an important class of Hopf algebras, of the sort
Milnor–Moore_theorem
State of a physical system in phase space
{a}}e^{-i\tau },{\hat {a}}^{\dagger }e^{i\tau }).} In this case, one can apply Bloch theorem to the n {\displaystyle n} -fold symmetric Hamiltonian and calculate
Phase_space_crystal
Blended wing body Blinking colloidal nanocrystals Bloch-Grüneisen temperature Bloch wall Bloch's theorem Bloch wave – MoM method Bloom (test) Blown flap Blue
Index_of_physics_articles_(B)
Decomposition of periodic functions
differentiable. ATS theorem Carleson's theorem Dirichlet kernel Discrete Fourier transform Fast Fourier transform Fejér's theorem Fourier analysis Fourier
Fourier_series
Generalisation of Jacobian variety
ISSN 0003-486X. JSTOR 1971109. MR 0577137. Bloch, Spencer (1979). "Torsion algebraic cycles and a theorem of Roitman". Compositio Mathematica. 39 (1)
Albanese_variety
Area of mathematics
known, but Andre Bloch conjectured and Hayman proved that one cannot dispose of an exceptional set. The Second Fundamental Theorem allows to give an
Nevanlinna_theory
American mathematician
ISBN 978-0-8218-5121-0. ISSN 1098-3627. Bloch, A. M.; Flaschka, H.; Rațiu, T. (1990-08-01). "A convexity theorem for isospectral manifolds of Jacobi matrices
Anthony_M._Bloch
In mathematics, the Bloch group is a cohomology group of the Bloch–Suslin complex, named after Spencer Bloch and Andrei Suslin. It is closely related to
Bloch_group
Gives the rank of the group of units in the ring of algebraic integers of a number field
In mathematics, Dirichlet's unit theorem is a basic result in algebraic number theory due to Peter Gustav Lejeune Dirichlet. It determines the rank of
Dirichlet's_unit_theorem
Theorem in quantum mechanics
flux quantum). The theorem was first stated and proven by Nina Byers and Chen-Ning Yang (1961), and further developed by Felix Bloch (1970). An enclosed
Byers–Yang_theorem
as of September 2022[update]. The conjecture terminology may persist: theorems often enough may still be referred to as conjectures, using the anachronistic
List_of_conjectures
Hungarian and American mathematician and physicist (1903–1957)
the application of this work was instrumental in his mean ergodic theorem. The theorem is about arbitrary one-parameter unitary groups t → V t {\displaystyle
John_von_Neumann
Concept in mathematics
them converges absolutely, then their Cauchy product converges to AB. The theorem is still valid in a Banach algebra (see first line of the following proof)
Cauchy_product
The unique homomorphic extension theorem is a result in mathematical logic which formalizes the intuition that the truth or falsity of a statement can
Unique homomorphic extension theorem
Unique_homomorphic_extension_theorem
Result in algebraic K-theory relating Chow groups to cohomology
In algebraic K-theory, a branch of mathematics, Bloch's formula, introduced by Spencer Bloch for K 2 {\displaystyle K_{2}} , states that the Chow group
Bloch's_formula
Statement that all non empty subsets of positive numbers contains a least element
a\in A\,(m\leq a)\right)\right]} . Most sources state this as an axiom or theorem about the natural numbers, but the phrase "natural number" was avoided
Well-ordering_principle
Fundamental principle of physics
in the main on this page and the quantum superposition. For example, the Bloch sphere to represent pure state of a two-level quantum mechanical system
Superposition_principle
Invariant of algebraic varieties and of more general schemes
different coefficients are related by the universal coefficient theorem, as in topology. By Bloch, Lichtenbaum, Friedlander, Suslin, and Levine, there is a
Motivic_cohomology
theorem Wigner 3-j symbols Wigner's 6-j symbols Wigner's 9-j symbols Wigner–Araki–Yanase theorem Wigner–Yanase–Dyson conjecture Wigner–Eckart theorem
List of things named after Eugene Wigner
List_of_things_named_after_Eugene_Wigner
Mathematical theory
especially striking result (conjectured earlier by André Bloch) is the Five Island theorem. Let D1,...,D5 be five Jordan regions on the Riemann sphere
Ahlfors_theory
Austrian mathematician (1884–1943)
mathematician after whom Helly's theorem, Helly families, Helly's selection theorem, Helly metric, and the Helly–Bray theorem were named. Helly earned his
Eduard_Helly
Subject area in mathematics
generated A-modules) Additive K-theory Bloch's formula Fundamental theorem of algebraic K-theory Basic theorems in algebraic K-theory K-theory K-theory
Algebraic_K-theory
Concept in geometry
topology. The notion is used in particular in the Riemann–Roch-type theorem. S. Bloch later generalized the notion in the context of arithmetic schemes
Localized_Chern_class
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