eigenfunction's Usage Examples:

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

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

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

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

The theorem stateswhere\hat{H}_{\lambda} is a Hamiltonian operator depending upon a continuous parameter \lambda\,,|\psi_\lambda\rangle, is an eigen-state (eigenfunction) of the Hamiltonian, depending implicitly upon \lambda,E_{\lambda}\, is the energy (eigenvalue) of the state |\psi_\lambda\rangle, i.

In MP theory the zeroth-order wave function is an exact eigenfunction of the Fock operator, which thus serves as the unperturbed operator.

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

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

Its eigenfunctions are | ϕ ⟩ {\displaystyle |\phi \rangle \,} and its eigenvalues are the.

This terminology is because the solutions correspond to the eigenvalues and eigenfunctions of a Hermitian.

solutions are the eigenfunctions associated to each λ.

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.

The complex-valued eigenfunctions of any linear time-invariant (LTI) system are of the following forms:.