1. A function that, when operated on by a linear operator, yields a scalar multiple of itself; a function whose form remains unchanged under a given mathematical operation except for multiplication by a constant.
Usage: technical; mathematics and physics; often used in quantum mechanics, differential equations, and linear algebra

Examples

• In quantum mechanics, the wave function of a particle in a definite energy state is an eigenfunction of the Hamiltonian operator.
• The eigenfunctions of the Laplacian operator are essential in solving boundary value problems.
• When you apply the differential operator to an eigenfunction, you get the same function multiplied by its eigenvalue.
• The sine and cosine functions are eigenfunctions of the second derivative operator.
• Physicists use eigenfunctions to describe the allowed states of a quantum system.