eigenfunction's Usage Examples:

In mathematics, an eigenfunction of a linear operator D defined on some function space is any non-zero function f in that space that, when acted upon.

It is also called energy eigenvector, energy eigenstate, energy eigenfunction, or energy eigenket.

the complex plane 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}}}.

spectral theory concerned with the determination of the spectrum and eigenfunction expansion associated with a linear ordinary differential equation.

If ψ is an eigenfunction of the operator A ^ {\displaystyle {\hat {A}}} , then A ^ ψ = a ψ ,.

is an orthonormal basis of the Hilbert space L2 that consists of the eigenfunctions of the autocovariance operator.

λ ⟩ {\displaystyle |\psi _{\lambda }\rangle } , is an eigen-state (eigenfunction) of the Hamiltonian, depending implicitly upon λ {\displaystyle \lambda.

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.

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

functions for a semisimple Lie group G also provide a set of simultaneous eigenfunctions for the natural action of the centre of the universal enveloping algebra.

Gel'fand introduced it in his work on eigenfunction expansions.

For all LTI systems, the eigenfunctions, and the basis functions of the transforms, are complex exponentials.

ergodic in the sense that the probability density associated to the nth eigenfunction of the Laplacian tends weakly to the uniform distribution on the unit.

\varphi _{\lambda }} is an eigenfunction associated with the eigenvalue λ {\displaystyle \lambda } .

Here the term "eigenfunction" is used to denote what.

increased norm squared) of an eigenfunction along unstable classical periodic orbits.

M and the vector v have been replaced by the kernel K(x, y) and the eigenfunction φ(y).

like a modular form under the action of the modular group, being an eigenfunction of the corresponding hyperbolic Laplace operator, and having at most.

q-exponential is a q-analog of the exponential function, namely the eigenfunction of a q-derivative.

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