In mathematics, an eigenfunction of a linear operator D defined on some function space is any non-zero function f {\displaystyle f} in that space that...

function such as x ↦ e i x , {\displaystyle x\mapsto e^{ix},} is an eigenfunction of the differential operator − i d d x {\displaystyle -i{\frac {d}{dx}}}...

Heath-Brown (1986) Eigenfunction Expansions Associated with Second-order Differential Equations. Part I (1946) 2nd. edition (1962); Eigenfunction Expansions Associated...

is an orthonormal basis of the Hilbert space L2 that consists of the eigenfunctions of the autocovariance operator. FPCA represents functional data in the...

energies). It is also called energy eigenvector, energy eigenstate, energy eigenfunction, or energy eigenket. It is very similar to the concept of atomic orbital...

to multiplication in the frequency domain. For all LTI systems, the eigenfunctions, and the basis functions of the transforms, are complex exponentials...

an infinite number of eigenvalues each with a unique eigenfunction, and that these eigenfunctions form an orthonormal basis of a certain Hilbert space...

In applied mathematics, the Hough functions are the eigenfunctions of Laplace's tidal equations which govern fluid motion on a rotating sphere. As such...

where K is a continuous function symmetric in x and y. The resulting eigenfunction expansion expresses the function K as a series of the form K ( x , y...

molecular wave function Ψs is also an eigenfunction of Lz with eigenvalue ±Λħ. Since Lz and Jz are equal, Ψs is an eigenfunction of Jz with same eigenvalue ±Λħ...

{\tfrac {d}{dx}}} , in which case the eigenvectors are functions called eigenfunctions that are scaled by that differential operator, such as d d x e λ x =...

(such as position, momentum, energy, angular momentum etc.). If ψ is an eigenfunction of the operator A ^ {\displaystyle {\hat {A}}} , then A ^ ψ = a ψ ,...

The overtones of a vibrating string are eigenfunctions of the second derivative, and form a harmonic progression. The associated eigenvalues form the arithmetic...

modes of vibration of an idealized circular drum head. These modes are eigenfunctions of a linear operator on a function space, a common construction in functional...

mathematical analysis, the Hilbert–Schmidt theorem, also known as the eigenfunction expansion theorem, is a fundamental result concerning compact, self-adjoint...

Hamiltonian. For a spin half nucleus there are two eigenfunctions for ÎZ. Let m = +1/2 and m = -1/2 and eigenfunctions are, ÎZ ψm = mħψm Applying the equation of...

cosine. The reason for this is that the exponential function is the eigenfunction of the operation of differentiation. In electrical engineering, signal...

eigenfunction solutions / eigenvector solutions to the Helmholtz equation / the matrix equation, often yield an orthogonal set of the eigenfunctions /...

mathematics, a Hecke eigensheaf is any sheaf whose value is based on an eigenfunction. It is an object that is a tensor-multiple of itself when formed under...

complete orthonormal system of eigenfunctions for the Fourier transform on L2(R). However, this choice of eigenfunctions is not unique. Because of F 4...

 b] consisting of eigenfunctions of TK such that the corresponding sequence of eigenvalues {λi}i is nonnegative. The eigenfunctions corresponding to non-zero...

operator consists of all eigenvalues λ for which there is a corresponding eigenfunction f with: − Δ f = λ f . {\displaystyle -\Delta f=\lambda f.} This is known...

negative of the differential operator with N(t) as the corresponding eigenfunction. The units of the decay constant are s−1[citation needed]. Given an...

potential system, if a wavefunction ψ ( r ) {\displaystyle \psi (r)} is an eigenfunction of the Hamiltonian operator H ^ ( p ^ , x ^ ) {\displaystyle {\hat {H}}({\hat...

upstream where a river is affected by tidal fluctuations Hough function – Eigenfunctions of Laplace's tidal equations which govern fluid motion on a rotating...

method is often surprisingly accurate. The next smallest eigenvalue and eigenfunction can be obtained by minimizing Q {\displaystyle Q} under the additional...

equation. Their solutions are based on eigenvalues and corresponding eigenfunctions of linear operators defined via second-order homogeneous linear equations...

the description of a particle with momentum exactly p, since it is an eigenfunction of the momentum operator. These functions are not normalizable to unity...

\in \Gamma } according to the given factor of automorphy j; to be an eigenfunction of certain Casimir operators on G; and to satisfy a "moderate growth"...

\mathbf {p} \psi (p)=p\psi (p)\,,} where the operator p acting on a wave eigenfunction ψ(p) yields that wave function multiplied by the eigenvalue p, in an...