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Hamilton's optical-mechanical analogy — Wikipedia (en)

Source: Wikipedia (en)
Original: https://en.wikipedia.org/wiki/Hamilton%27s_optical-mechanical_analogy
License (as archived): CC-BY-SA-4.0
Archived: 2026-10-07T13:44:46.586Z
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Hamilton's optical-mechanical analogy — Wikipedia (en) — Wikipedia (en), https://en.wikipedia.org/wiki/Hamilton%27s_optical-mechanical_analogy (CC-BY-SA-4.0); archived copy: https://metraipolis.com/documento/dc_7eeedd65bcdd (Metraipolis archive dc_7eeedd65bcdd, sha256 6400e016e4ed8d332cafd1d8f53757b9b32cc1e1c0857691dbedb3ef0a72ca12)

BibTeX

@misc{dc7eeedd65bcdd,
  title = {Hamilton's optical-mechanical analogy — Wikipedia (en)},
  howpublished = {Wikipedia (en)},
  url = {https://en.wikipedia.org/wiki/Hamilton%27s_optical-mechanical_analogy},
  note = {License CC-BY-SA-4.0; archived copy https://metraipolis.com/documento/dc_7eeedd65bcdd; sha256 6400e016e4ed8d332cafd1d8f53757b9b32cc1e1c0857691dbedb3ef0a72ca12},
  year = {2026}
}

Archived text

Reproduced under CC-BY-SA-4.0. Attribution: Wikipedia (en), https://en.wikipedia.org/wiki/Hamilton%27s_optical-mechanical_analogy. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

Hamilton's optical-mechanical analogy (also written Hamilton's optico-mechanical analogy) is a conceptual parallel between trajectories in classical mechanics and wavefronts in optics, introduced by William Rowan Hamilton around 1831. It may be viewed as linking Huygens' principle of optics with Maupertuis' principle of mechanics. While Hamilton discovered the analogy in 1831, it was not applied practically until Hans Busch used it to explain electron beam focusing in 1925. According to Cornelius Lanczos, the analogy has been important in the development of ideas in quantum physics. Erwin Schrödinger cites the analogy in the very first sentence of his paper introducing his wave mechanics. Later in the body of his paper he says: Unfortunately this powerful and momentous conception of Hamilton is deprived, in most modern reproductions, of its beautiful raiment as a superfluous accessory, in favour of a more colourless representation of the analytical correspondence. Quantitative and formal analysis based on the analogy use the Hamilton–Jacobi equation; conversely the analogy provides an alternative and more accessible path for introducing the Hamilton–Jacobi equation approach to mechanics. The orthogonality of mechanical trajectories characteristic of geometrical optics to the optical wavefronts characteristic of a full wave equation, resulting from the variational principle, leads to the corresponding differential equations.

Tema degli esploratori: fisica e astronomia (deposito sistematico; categoria «Quantum mechanics»).
Fonte: Wikipedia in inglese, voce «Hamilton's optical-mechanical analogy» — https://en.wikipedia.org/wiki/Hamilton%27s_optical-mechanical_analogy
Wikidata Q18648936: «Conceptual parallel between optics and classical mechanics» (dati Wikidata in CC0 1.0) — https://www.wikidata.org/wiki/Q18648936
Autori: i contributori di Wikipedia (cronologia: https://en.wikipedia.org/wiki/Hamilton%27s_optical-mechanical_analogy?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 1357468108, consultata il 2026-10-07T13:17:39.337Z tramite l'API ufficiale di Wikipedia. Impronta SHA-256 dell'estratto: d38d213da9bb9fc4b8ff3a4a4aa4c7c9cd7932cf0edbef2e6eeaa3a39db01d34