Eigenfunction
From Wikipedia, the free encyclopedia.
In
mathematics, an
eigenfunction f of a
linear operator A on a
function space is an
eigenvector of the linear operator; it satisfies
for some
scalar λ, the corresponding
eigenvalue. The existence of eigenvectors is typically a great help in analysing
A.
For example, is an eigenfunction for the differential operator
for any value of , with a corresponding eigenvalue .
Eigenfunctions play an important role in quantum mechanics, where the Schrödinger equation
has solutions of the form
where are eigenfunctions of the operator with eigenvalues . Due to the nature of the
hamiltonian operator , its eigenfunctions are
orthogonal functions. This is not necessarily the case for eigenfunctions of other operators (such as the example mentioned above)
