Metraipolis › archive › dc_f648aa4307bb

Helmholtz equation — Wikipedia (en)

Source: Wikipedia (en)
Original: https://en.wikipedia.org/wiki/Helmholtz_equation
License (as archived): CC-BY-SA-4.0
Archived: 2026-10-15T14:37:05.575Z
SHA-256 of the archived text: 26b3a4cf3ffe6ad4b2ec08f52bd4ee674b6100c89257038a57862f99bfb85009
Stable URL of this page: https://metraipolis.com/documento/dc_f648aa4307bb

How to cite

Helmholtz equation — Wikipedia (en) — Wikipedia (en), https://en.wikipedia.org/wiki/Helmholtz_equation (CC-BY-SA-4.0); archived copy: https://metraipolis.com/documento/dc_f648aa4307bb (Metraipolis archive dc_f648aa4307bb, sha256 26b3a4cf3ffe6ad4b2ec08f52bd4ee674b6100c89257038a57862f99bfb85009)

BibTeX

@misc{dcf648aa4307bb,
  title = {Helmholtz equation — Wikipedia (en)},
  howpublished = {Wikipedia (en)},
  url = {https://en.wikipedia.org/wiki/Helmholtz_equation},
  note = {License CC-BY-SA-4.0; archived copy https://metraipolis.com/documento/dc_f648aa4307bb; sha256 26b3a4cf3ffe6ad4b2ec08f52bd4ee674b6100c89257038a57862f99bfb85009},
  year = {2026}
}

Archived text

Reproduced under CC-BY-SA-4.0. Attribution: Wikipedia (en), https://en.wikipedia.org/wiki/Helmholtz_equation. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

In mathematics, the Helmholtz equation is the eigenvalue problem for the Laplace operator. It corresponds to the elliptic partial differential equation: ∇ 2 f = − k 2 f , {\displaystyle \nabla ^{2}f=-k^{2}f,} where ∇2 is the Laplace operator, –k2 is the eigenvalue, and f is the (eigen)function. When the equation is applied to waves, k is known as the wave number. The Helmholtz equation has a variety of applications in physics and other sciences, including the wave equation, the diffusion equation, and the Schrödinger equation for a free particle. In optics, the Helmholtz equation is the wave equation for the electric field. The equation is named after Hermann von Helmholtz, who studied it in 1860.

Tema degli esploratori: matematica e informatica teorica (deposito sistematico; ricerca «differential equation»).
Fonte: Wikipedia in inglese, voce «Helmholtz equation» — https://en.wikipedia.org/wiki/Helmholtz_equation
Wikidata Q860615 (dati Wikidata in CC0 1.0) — https://www.wikidata.org/wiki/Q860615
Autori: i contributori di Wikipedia (cronologia: https://en.wikipedia.org/wiki/Helmholtz_equation?action=history).
Licenza: Creative Commons Attribuzione-Condividi allo stesso modo 4.0 (CC BY-SA 4.0) — https://creativecommons.org/licenses/by-sa/4.0/. Il riuso richiede attribuzione e stessa licenza.
Estratto dell'introduzione non modificato nel contenuto; revisione 1365786888, consultata il 2026-10-15T13:58:38.633Z tramite l'API ufficiale di Wikipedia. Impronta SHA-256 dell'estratto: 29b39cfef24b4b1b6c8cd3189ccf89e4c7deff533edb734ad068d444c18ed4ee