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- Mehler_kernel abstract "In mathematics and physics, the Mehler kernel is the fundamental solution, or non-relativistic propagator of the Hamiltonian for the quantum harmonic oscillator.Mehler (1866) gave an explicit formula for it, called Mehler's formula. The Mehler kernel provides the fundamental solution for the most general solution φ(x, y; t) to Specifically, Mehler's kernel is By a simple transformation, this is, apart from a multiplying factor, the bivariate Gaussian probability density given byWhen t=0 variables x and y coincide resulting in the formulaThe bivariate probability density can be written as an infinite series involving the one-dimensional probability densities and Hermite polynomials of x and y. The Kibble–Slepian formula generalizes this expansion to higher dimensions.".
- Mehler_kernel wikiPageExternalLink books?id=X7QQcVa2EWsC.
- Mehler_kernel wikiPageExternalLink purl?GDZPPN002152975.
- Mehler_kernel wikiPageID "31393808".
- Mehler_kernel wikiPageRevisionID "599329695".
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- Mehler_kernel hasPhotoCollection Mehler_kernel.
- Mehler_kernel indent "::".
- Mehler_kernel subject Category:Parabolic_partial_differential_equations.
- Mehler_kernel type Abstraction100002137.
- Mehler_kernel type Communication100033020.
- Mehler_kernel type DifferentialEquation106670521.
- Mehler_kernel type Equation106669864.
- Mehler_kernel type MathematicalStatement106732169.
- Mehler_kernel type Message106598915.
- Mehler_kernel type ParabolicPartialDifferentialEquations.
- Mehler_kernel type PartialDifferentialEquation106670866.
- Mehler_kernel type Statement106722453.
- Mehler_kernel comment "In mathematics and physics, the Mehler kernel is the fundamental solution, or non-relativistic propagator of the Hamiltonian for the quantum harmonic oscillator.Mehler (1866) gave an explicit formula for it, called Mehler's formula.".
- Mehler_kernel label "Mehler kernel".
- Mehler_kernel sameAs m.0gk_bls.
- Mehler_kernel sameAs Q6809515.
- Mehler_kernel sameAs Q6809515.
- Mehler_kernel sameAs Mehler_kernel.
- Mehler_kernel wasDerivedFrom Mehler_kernel?oldid=599329695.
- Mehler_kernel isPrimaryTopicOf Mehler_kernel.