Eigenfunction expansion

1. What is eigenfunction expansion?
2. What is the meaning of eigenfunction?
3. What is Orthonormality of eigenfunctions?

What is eigenfunction expansion?

The eigenfunction expansion technique requires that the problem be linear; for all functions y and w satisfying the boundary conditions and all scalar values α, (a) L(y + w) = L(y) + L(w) (b) L(αy) = αL(y) (c) (y + w) and αy satisfy the boundary conditions.

What is the meaning of eigenfunction?

In mathematics, an eigenfunction of a linear operator D defined on some function space is any non-zero function in that space that, when acted upon by D, is only multiplied by some scaling factor called an eigenvalue.

What is Orthonormality of eigenfunctions?

Eigenfunctions of a Hermitian operator are orthogonal if they have different eigenvalues. Because of this theorem, we can identify orthogonal functions easily without having to integrate or conduct an analysis based on symmetry or other considerations.