• theory, the d'Alembert operator (denoted by a box: ◻ {\displaystyle \Box } ), also called the d'Alembertian, wave operator, box operator or sometimes...
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  • Thumbnail for Jean le Rond d'Alembert
    Jean-Baptiste le Rond d'Alembert (/ˌdæləmˈbɛər/ DAL-əm-BAIR; French: [ʒɑ̃ batist lə ʁɔ̃ dalɑ̃bɛʁ]; 16 November 1717 – 29 October 1783) was a French mathematician...
    30 KB (2,931 words) - 03:00, 6 September 2024
  • high-energy particle physics. The D'Alembert operator is also known as the wave operator because it is the differential operator appearing in the wave equations...
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  • vector operator, as seen above in the case of the Laplacian. del d'Alembert operator H. M. Schey (1996) Div, Grad, Curl, and All That: An Informal Text...
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  • between any two bounds always results in 0. D'Alembert operator Mechanical wave Wave equation D'Alembert (1747) "Recherches sur la courbe que forme une...
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  • d'Alembert may refer to: Jean le Rond d'Alembert the d'Alembert operator, named after the former d'Alembert's principle, also named after the above d'Alembert's...
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  • radical 31, "enclosure") ◻ {\displaystyle \Box } , the symbol of the D'Alembert operator Square (astrological aspect), an aspect of 90 degrees Square (dessert)...
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  • after Jean d'Alembert: d'Alembert criterion d'Alembert force d'Alembert operator d'Alembertian d’Alembert reduction d'Alembert system d'Alembert's equation...
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  • Thumbnail for Wave equation
    time, Δ {\displaystyle \Delta } is the Laplace operator and ◻ {\displaystyle \Box } the d'Alembert operator, defined as: u t t = ∂ 2 u ∂ t 2 , Δ = ∂ 2 ∂...
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  • Thumbnail for Inhomogeneous electromagnetic wave equation
    left hand sides of each equation correspond to wave motion (the D'Alembert operator acting on the fields), while the right hand sides are the wave sources...
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  • of edges leaving S, which defines a cut. d'Alembert operator Differentiable programming Differential operator § Notations List of mathematical symbols...
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  • Thumbnail for Green's function
    L=\square ={\tfrac {1}{c^{2}}}\partial _{t}^{2}-\nabla ^{2}} , the d'Alembert operator, and space has 3 dimensions then: [ [ L ] ] = [ [ length ] ] − 2...
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  • environment □ ("box") operator in mathematics, used for: Logical necessity in modal logic Conway box function D'Alembert operator Rectangular cuboid, a...
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  • Thumbnail for Maxwell's equations
    used to raise and lower indices is ηαβ = diag(1, −1, −1, −1). The d'Alembert operator on Minkowski space is ◻ = ∂α∂α as in the vector formulation. In general...
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  • {\displaystyle \partial y/\partial x} ) ◻ {\displaystyle \Box } D'Alembert operator ∇ 2 − ∂ t 2 {\displaystyle \nabla ^{2}-\partial _{t}^{2}} ⟨ ⟩ {\displaystyle...
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  • Thumbnail for Electromagnetic radiation
    {\displaystyle \Box f=0} where ◻ {\displaystyle \Box } denotes the so-called d'Alembert operator, which in Cartesian coordinates is given as: ◻ = ∇ 2 − 1 c 0 2 ∂...
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  • ^{2}-{\frac {1}{c^{2}}}{\frac {\partial ^{2}}{\partial t^{2}}}} is the d'Alembert operator. The electromagnetic wave equation is modified in two ways, the derivative...
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  • Thumbnail for Retarded potential
    and current density J(r, t), and ◻ {\displaystyle \Box } is the D'Alembert operator. Solving these gives the retarded potentials below (all in SI units)...
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  • ∂ μ ∂ μ {\displaystyle \partial ^{\mu }\partial _{\mu }} as the d'Alembert operator). In GR, one must use the more general metric tensor g α β {\displaystyle...
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  • The fundamental theorem of algebra, also called d'Alembert's theorem or the d'Alembert–Gauss theorem, states that every non-constant single-variable polynomial...
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  • Partial derivative (category Differential operators)
    d'Alembert operator Chain rule Curl (mathematics) Divergence Exterior derivative Iterated integral Jacobian matrix and determinant Laplace operator Multivariable...
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  • Thumbnail for Proca action
    }}\right)^{2}\mathbf {A} \!} and ◻ {\displaystyle \Box } is the D'Alembert operator. The Proca action is the gauge-fixed version of the Stueckelberg...
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  • electromagnetism and wave theory, the d'Alembert operator ( ◻ {\displaystyle \scriptstyle \Box } ) is the Laplace operator of Minkowski space. The Levi-Civita...
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  • mathematical and physical condition D'Alembert operator, an operator of the Einstein equation Ratio test, also known as d'Alembert's test, a test for the convergence...
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  • ^{2}(|u|_{}^{2})\end{aligned}}} where ◻ {\displaystyle \Box } is the d'Alembert operator. Resonant interaction; the Zakharov equation describes non-linear...
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  • Mahecha, in the relativistic case, the quantum potential (using the d'Alembert operator  ◻ {\displaystyle \scriptstyle \Box } and in the notation ℏ = 1 {\displaystyle...
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  • calculations in Minkowski space, the d'Alembert operator, also called the d'Alembertian, wave operator, or box operator is represented as ◻ {\displaystyle...
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  • \square =\eta ^{\mu \nu }\partial _{\mu }\partial _{\nu }} is the d'Alembert operator. Together with the Ricci scalar, R = η μ ν R μ ν = ∂ μ ∂ ν h μ ν...
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  • Thumbnail for Four-current
    A^{\alpha }=\mu _{0}J^{\alpha }} where ◻ {\displaystyle \Box } is the D'Alembert operator, or the electromagnetic field tensor: ∇ α F α β = μ 0 J β {\displaystyle...
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  • Thumbnail for Post-Newtonian expansion
    {E}}_{i}+2{\tilde {E}}_{ij}} where ◻ {\displaystyle \Box } is the d'Alembert operator, E {\displaystyle E} is a scalar, E ^ i {\displaystyle {\hat {E}}_{i}}...
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