In condensed matter physics, Bloch's theorem states that solutions to the Schrödinger equation in a periodic potential can be expressed as plane waves...
36 KB (6,052 words) - 07:43, 21 May 2024
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...
8 KB (1,165 words) - 01:16, 26 September 2024
Crystal momentum (redirect from Bloch momentum)
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 ) =...
12 KB (1,474 words) - 19:16, 9 July 2024
periodic function, with the same periodicity as the crystal lattice. Bloch's theorem proves that the solutions to this differential equation can be written...
12 KB (1,975 words) - 11:29, 25 March 2024
Translation operator (quantum mechanics) (section Discrete translation in periodic potential: Bloch's theorem)
{k} \cdot \mathbf {R} }\psi (\mathbf {r} )} This result is known as Bloch's Theorem. In the passive transformation picture, translational invariance requires...
31 KB (5,662 words) - 11:32, 18 May 2024
Floquet theory (redirect from Floquet's theorem)
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...
9 KB (1,315 words) - 07:00, 23 July 2024
Fourier series (redirect from Fourier theorem)
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...
70 KB (10,863 words) - 12:21, 11 September 2024
periodic potential. The solutions in this case are known as Bloch states. Since Bloch's theorem applies only to periodic potentials, and since unceasing...
10 KB (1,164 words) - 23:06, 11 January 2024
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...
9 KB (1,048 words) - 16:54, 17 September 2024
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...
11 KB (640 words) - 06:31, 24 September 2024