Also found in: Dictionary, Encyclopedia, Wikipedia.
Related to eigenfunction: eigenfunction expansion


A solution of a differentiated equation that has solutions only for particular values of some parameters. Compare: eigenvalue.
[Ger. eigen, particular, peculiar to]
Mentioned in ?
References in periodicals archive ?
A solution of differential equation of motion was assumed as a product of eigenfunctions of displacement and time [2, 3]:
Observe that f itself is a right eigenfunction, that corresponding to the partition with single part.
If this eigenfunction representation of M(x) is operated upon by D, the unknown coefficients can be found easily from the equation itself:
To begin with, any THT eigenfunction satisfies the inequality
m] be the normalized positive eigenfunction associated to the first positive eigenvalue [[lambda].
The way to do that is to calculate the eigenfunction for the lowest n and l by iterating n = 0;1;2; : : : and taking l = 1,2, .
12) modifies accordingly, and if [PSI] denotes the eigenfunction that is related to the unchanged eigenvalue [?
1] allows 0 as an eigenvalue, the corresponding eigenfunction [psi] being positive.
An example is the extension of the Taylor-Aris theory for dispersion during laminar flow in a tube (53, 54, 55), where he showed that the Taylor-Aris expression for the effective longitudinal dispersion coefficient corresponds to retention of only the leading term of an eigenfunction expansion of the full solution.
Organization is in eight chapters covering linear equations, systems of linear first order equations, power series solutions, adjoint operators and nonhomogeneous boundary value problems, green functions, eigenfunction expansions, long time behavior of systems of differential equations, and existence and uniqueness theorems.