Dictionary

eigenfunction en · NOUN

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-der. Proto-Italic *fungōr Latin fungor 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.

Meanings

1. A function ϕ such that, for a given linear operator D, Dϕ=λϕ for some scalar λ (called an eigenvalue).
   • 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. 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:
   • 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. 2005, Leonid D. Akulenko, Sergei V. Nesterov, High-Precision Methods in Eigenvalue Problems and Their Applications, CRC Press (Chapman & Hall), page 1:

Forms

Relateds

eigendecomposition · eigensystem · eigenbrain · eigentheory · eigen decomposition · eigenmode · eigenvalue · eigenstate · eigenhead · eigenspace · eigenspinor · eigenpair · hamiltonian · eigenface · eigenvector · eigenbasis

Synonyms

eigenstate · proper function

Translations (16)

pt função própria (function) · el ιδιοσυνάρτηση (function) · es función propia (function) · sv egenfunktion (function) · fi ominaisfunktio (function) · is eiginfall (function) · de Eigenfunktion (function) · cmn 本徵函數 /本征函数 (function) · fr fonction propre (function) · pl równanie własne (function) · it autofunzione (function) · ja 固有関数 (function) · es autofunción (function) · ru со́бственная фу́нкция (function) · pt autofunção (function) · cy ffwythiant eigen (function)