GeezerVison

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English

Etymology

Etymology tree

Proto-Indo-European *h₂eyḱ-

Proto-Indo-European *h₂eh₂óyḱe

Proto-Germanic *aiganą

Proto-Germanic *aiganaz

Proto-West Germanic *aigan

Old High German eigan

Middle High German eigen

German eigenbor.

English eigen-

Proto-Indo-European *bʰewg-

Proto-Indo-European *-né-

Proto-Indo-European *-ti

Proto-Indo-European *bʰunégti

Proto-Italic *fungōr

Latin fungor

Proto-Indo-European *-tós

Proto-Indo-European *-is

Proto-Indo-European *-tis

Proto-Indo-European *-Hō

Proto-Indo-European *-tiHō

Proto-Italic *-tiō

Latin -tiō

Latin fūnctiō

Old French fonction

Middle French functionbor.

English function

English eigenfunction

From eigen- + function.

Noun

eigenfunction (plural eigenfunctions)

(mathematics) A function ϕ such that, for a given linear operator D, Dϕ=λϕ for some scalar λ (called an eigenvalue).
- 2000, John von Neumann, E. Wigner, “On the Behaviour of Eigenvalues in Adiabatic Processes”, in Hinne Hettema, transl., edited by Hinne Hettema, Quantum Chemistry: Classic Scientific Papers, World Scientific, published 1929, page 25:
  For many quantum-mechanical problems it is important to investigate the change of eigenvalues and eigenfunctions with the continuous change of one or more parameters. The case in which one knows the eigenvalues and eigenfunctions for two special values of the parameters, and is interested in the region in between is particularly interesting.
- 2005, Leonid D. Akulenko, Sergei V. Nesterov, High-Precision Methods in Eigenvalue Problems and Their Applications‎^[1], CRC Press (Chapman & Hall), page 1:
  Problems that require an investigation of eigenvalues and eigenfunctions arise in connection with numerous topics in mechanics, the theory of vibrations and stability, hydrodynamics, elasticity, acoustics, electrodynamics, quantum mechanics, etc.

Synonyms

proper function, eigenstate

Related terms

Translations

function

Arabic: ^{(please verify)} دَالَة خَاصَّة f (dāla ḵāṣṣa)
Chinese:
Mandarin: 本徵函數 / 本征函数 (běnzhēng hánshù)
Finnish: ominaisfunktio
French: fonction propre (fr) f
German: Eigenfunktion (de) f
Greek: ιδιοσυνάρτηση f (idiosynártisi)
Icelandic: eiginfall n
Italian: autofunzione (it) f
Japanese: 固有関数 (ja) (koyū kansū)
Polish: równanie własne n
Portuguese: autofunção f (Brazil), função própria f (Portugal)
Russian: со́бственная фу́нкция f (sóbstvennaja fúnkcija)
Spanish: autofunción f, función propia f
Swedish: egenfunktion (sv) c
Welsh: ffwythiant eigen m