The Eigenfunction reference article from the English Wikipedia on 24-Jul-2004 (provided by Fixed Reference: snapshots of Wikipedia from wikipedia.org)

Eigenfunction

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)

This is the "Eigenfunction" reference article from the English Wikipedia. All text is available under the terms of the GNU Free Documentation License. See also our Disclaimer.