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Pronunciation varies by accent · noun
(mathematics) 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.
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.
Use eigenfunction when its meaning, tone and grammar fit the full sentence. A synonym is not always a direct replacement.
Eigenfunction means (mathematics) A function ϕ such that, for a given linear operator D, Dϕ=λϕ for some scalar λ (called an eigenvalue)..
Common synonyms include proper function, eigenstate.
The opposite depends on the specific sense.
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.
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