In condensed matter physics, Bloch's theorem states that solutions to the Schrödinger equation in a periodic potential can be expressed as plane waves...

function theorem. The number B is called the Bloch's constant. The lower bound 1/72 in Bloch's theorem is not the best possible. Bloch's theorem tells us...

periodic function, with the same periodicity as the crystal lattice. Bloch's theorem proves that the solutions to this differential equation can be written...

special case of electron waves in a periodic crystal lattice using Bloch's theorem as treated generally in the dynamical theory of diffraction. Every...

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...

periodic potential. The solutions in this case are known as Bloch states. Since Bloch's theorem applies only to periodic potentials, and since unceasing...

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...

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...

a simple kinetic-plus-potential form.: 134  These conditions imply Bloch's theorem, which states ψ n ( x ) = e i k ⋅ x u n k ( x ) , u n k ( x + a ) =...

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...

{k} \cdot \mathbf {R} }\psi (\mathbf {r} )} This result is known as Bloch's Theorem. In the passive transformation picture, translational invariance requires...

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...

Arakelyan's theorem (complex analysis) Area theorem (conformal mapping) (complex analysis) Beurling–Lax theorem (Hardy spaces) Bloch's theorem (complex analysis)...

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...

quantum-mechanical justification was given a year later (1928) by Bloch's theorem: an unbound electron moves in a periodic potential as a free electron...

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...

In mathematics, the norm residue isomorphism theorem is a long-sought result relating Milnor K-theory and Galois cohomology. The result has a relatively...

independent electron approximation is still in effect. As shown by Bloch's theorem, introducing a periodic potential into the Schrödinger equation results...

physics, Nanoscale and mesoscopic physics, Polymer physics BCS theory, Bloch's theorem, Density functional theory, Fermi gas, Fermi liquid theory, Many-body...

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...

physics, Nanoscale and mesoscopic physics, Polymer physics BCS theory, Bloch's theorem, Density functional theory, Fermi gas, Fermi liquid theory, Many-body...

which the effect had first been observed. Anderson impurity model Bloch's theorem Electronic band structure Solid-state physics Bose–Hubbard model t-J...

necessarily true. A further generalization appears in the context of Bloch's theorems and Floquet theory, which govern the solution of various periodic differential...

Schrödinger equation is often written for functions of momentum, as Bloch's theorem ensures the periodic crystal lattice potential couples Ψ ~ ( p ) {\displaystyle...

condition and plugging in Schrödinger's equation results in a proof of Bloch's theorem, which is particularly important in understanding the band structure...

In quantum mechanics and computing, the Bloch sphere is a geometrical representation of the pure state space of a two-level quantum mechanical system...

quasiperiods, the periods of the corresponding Weierstrass ℘ function. Bloch's theorem says that the eigenfunctions of a periodic Schrödinger equation (or...

periodicity of the crystalline potential allows the application of the Bloch theorem, which states that the Hamiltonian eigenstates take the form ψ n k (...

Center near Mountain View, California. With the publication of Bloch's book, Ginsberg's theorem seemingly thereafter became much more widely known. Robert...

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...