What does eigenfunction mean?
An eigenfunction is a function that, when acted upon by a linear operator, results in a scaled version of itself. This concept is crucial in mathematics and physics, particularly in the study of linear differential equations and quantum mechanics. Eigenfunctions are used to describe the wave functions of quantum systems and are essential in solving problems involving linear operators. The term is often used interchangeably with eigenvector function or characteristic function. Understanding eigenfunctions is vital for working with linear transformations and differential equations.
nounA function that, when operated on by a linear operator, results in a scaled version of itself.
- A function that is a solution to a linear differential equation.
- A function that satisfies a certain equation involving a linear operator.
"The eigenfunction of the Hamiltonian operator is a wave function that describes a quantum system."
"The eigenfunction of the Laplacian operator is a harmonic function."
"The eigenfunction of the Fourier transform is a Gaussian function."
The plural form is used when referring to multiple eigenfunctions.
"The eigenfunctions of the Hamiltonian operator are used to describe the energy states of a quantum system."
Reviewed by Deb Chak, Editor. AI-assisted content curated by RJS Tech Solutions LLP.
Etymology of eigenfunction
The term 'eigenfunction' originates from the German words 'eigen,' meaning 'own' or 'proper,' and 'function.' It is related to the concept of eigenvalues and eigenvectors in linear algebra. The term has been used in mathematics and physics since the early 20th century.
Usage notes
Typically used in mathematics, physics, and engineering contexts.