generalized eigenfunction

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• Generalized function — In mathematics, generalized functions are objects generalizing the notion of functions. There is more than one recognised theory. Generalized functions are especially useful in making discontinuous functions more like smooth functions, and (going …   Wikipedia

• Generalized eigenvector — In linear algebra, a generalized eigenvector of a matrix A is a nonzero vector v, which has associated with it an eigenvalue lambda; having algebraic multiplicity k ge;1, satisfying: (A lambda I)^kmathbf{v} = mathbf{0}.Ordinary eigenvectors are… …   Wikipedia

• Rigged Hilbert space — In mathematics, a rigged Hilbert space (Gelfand triple, nested Hilbert space, equipped Hilbert space) is a construction designed to link the distribution and square integrable aspects of functional analysis. Such spaces were introduced to study… …   Wikipedia

• Spectral theory — In mathematics, spectral theory is an inclusive term for theories extending the eigenvector and eigenvalue theory of a single square matrix. The name was introduced by David Hilbert in his original formulation of Hilbert space theory, which was… …   Wikipedia

• Eigenvalues and eigenvectors — For more specific information regarding the eigenvalues and eigenvectors of matrices, see Eigendecomposition of a matrix. In this shear mapping the red arrow changes direction but the blue arrow does not. Therefore the blue arrow is an… …   Wikipedia

• Wave function — Not to be confused with the related concept of the Wave equation Some trajectories of a harmonic oscillator (a ball attached to a spring) in classical mechanics (A B) and quantum mechanics (C H). In quantum mechanics (C H), the ball has a wave… …   Wikipedia

• Particle in a spherically symmetric potential — In quantum mechanics, the particle in a spherically symmetric potential describes the dynamics of a particle in a potential which has spherical symmetry. The Hamiltonian for such a system has the form:hat{H} = frac{hat{p}^2}{2m 0} + V(r)where m 0 …   Wikipedia

• Spectral theory of ordinary differential equations — In mathematics, the spectral theory of ordinary differential equations is concerned with the determination of the spectrum and eigenfunction expansion associated with a linear ordinary differential equation. In his dissertation Hermann Weyl… …   Wikipedia

• Hilbert space — For the Hilbert space filling curve, see Hilbert curve. Hilbert spaces can be used to study the harmonics of vibrating strings. The mathematical concept of a Hilbert space, named after David Hilbert, generalizes the notion of Euclidean space. It… …   Wikipedia

• Eigenvalue, eigenvector and eigenspace — In mathematics, given a linear transformation, an Audio|De eigenvector.ogg|eigenvector of that linear transformation is a nonzero vector which, when that transformation is applied to it, changes in length, but not direction. For each eigenvector… …   Wikipedia

• Normal distribution — This article is about the univariate normal distribution. For normally distributed vectors, see Multivariate normal distribution. Probability density function The red line is the standard normal distribution Cumulative distribution function …   Wikipedia