1. Functions that satisfy a differential or integral equation and remain essentially unchanged (up to a scalar multiple) when a linear operator is applied to them; used extensively in physics, engineering, and mathematics.
Usage: technical; mathematics; physics; plural form of eigenfunction

Examples

• The eigenfunctions of the Schrödinger equation describe the allowed quantum states of a particle.
• In vibration analysis, eigenfunctions represent the natural modes of oscillation of a structure.
• The eigenfunctions of a Sturm-Liouville problem form an orthogonal basis for function spaces.
• Engineers use eigenfunctions to solve boundary value problems in heat conduction and wave propagation.
• The eigenfunctions corresponding to different eigenvalues are orthogonal to each other.