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...

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

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...

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...

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 ) =...

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...

is useful to make the Fourier series of the potential when applying Bloch's theorem. First, we may write any arbitrary position vector r {\displaystyle...

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