eigenfunction

1 9.9

A function that a mathematical operation only multiplies by a number without changing its form

noun
/ˈaɪɡənˌfʌŋkʃən/

Specialized

: función propia

An eigenfunction is essential in solving differential equations in quantum mechanics.

There exists some complete set of eigenfunctions of that operator.

Examples

So the answer is you have an angular momentum eigenfunction no matter what.
Since the wave function includes all the necessary information about considering systems, the energy eigenvalues and corresponding eigenfunctions between interaction systems in relativistic quantum mechanics and in nonrelativistic quantum mechanics have been studied more efficiently in recent years.

Blog text (6)
If you have a pure eigenfunction, you have standing waves.
All right, The cosine is not an eigenfunction, but it's close.
So these are indeed eigenfunctions of the X operator.
The decomposition Eq. (11) is an expansion in eigenfunctions of the graph Laplacian of the hypercube, which is also known as a Walsh transform in computer science.

Academic text (2018)
In linear algebra, each eigenfunction corresponds to a specific eigenvalue of a matrix.
To understand wave behavior, we study how an eigenfunction changes under various operators.

Surface Forms

eigenfunction singular

eigenfunctions plural

Morphology

eigenfunction = function (opaque) = eigen + function

The combining form 'eigen-' is a German borrowing used in technical mathematics and is not a productive or semantically transparent prefix for average learners, so the precise meaning cannot be derived from 'function' alone.

Etymology

Eigenfunction combines the German eigen meaning 'own' and the English function. So an eigenfunction is a function that stays 'itself' when a mathematical rule acts on it, because it is only multiplied by a number and not otherwise changed.