eigenfunctions love

# eigenfunctions

## Definitions

• noun Plural form of eigenfunction.

## Etymologies

Sorry, no etymologies found.

## Examples

• This pure chance process will quickly drive macroscopic systems into near eigenfunctions of position while leaving isolated micro-systems in superposition states.

Philosophy of Statistical Mechanics Sklar, Lawrence 2009

• Nr (k) are the integers nr (k) = 0, 1, 2, ¦ and the corresponding eigenfunctions (up to a normalisation factor) are

Quantum Field Theory Kuhlmann, Meinard 2006

• You and I know that as the first few eigenfunctions.

• These closed objects are commonly called spherical harmonics, although they are only remotely related to the mathematical definition found in the solution to certain wave functions, most notably the eigenfunctions of angular momentum operators.

UNEASYsilence 2010

• You and I know that as the first few eigenfunctions.

• In German the functions are called spherical harmonics appear as eigenfunctions of [[Angular momentum (quantum) #Orbital angular momentum | orbital angular momentum]].

• Characters behave in a very simple manner with respect to translation (indeed, they are eigenfunctions of the translation action), and so the Fourier transform tends to simplify any mathematical problem which enjoys a translation invariance symmetry (or an approximation to such a symmetry).

What's new 2009

• In [[quantum mechanics]] spherical harmonics appear as eigenfunctions of [[Angular momentum (quantum) #Orbital angular momentum | orbital angular momentum]].

• Since you've used the words eigenfunctions / eigenvalues / eigenstates in quite a few articles that I am aware of, why not create the definition subpage for the

• Rather than using parameteric basis functions to perform the spatial interpolation, you are instead using non-parametric basis functions which are eigenfunctions of the covariance matrix of the data.

RealClimate 2009