D'Alembert operator
In special relativity, electromagnetism and wave theory, the d'Alembert operator (denoted by a box: ), also called the d'Alembertian, wave operator, box operator or sometimes quabla operator (cf. nabla symbol) is the Laplace operator of Minkowski space. The operator is named after French mathematician and physicist Jean le Rond d'Alembert. In Minkowski space, in standard coordinates (t, x, y, z), it has the form Here is the 3-dimensional Laplacian and ημν is the inverse Minkowski metric with , , for . (Some authors alternatively use the negative metric signature of (− + + +), with .)
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- Function113783816
- MathematicalRelation113783581
- MathematicalStatement106732169
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- PartialDifferentialEquation106670866
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- WikicatDifferentialOperators
- WikicatHyperbolicPartialDifferentialEquations
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- enIn special relativity, electromagnetism and wave theory, the d'Alembert operator (denoted by a box: ), also called the d'Alembertian, wave operator, box operator or sometimes quabla operator (cf. nabla symbol) is the Laplace operator of Minkowski space. The operator is named after French mathematician and physicist Jean le Rond d'Alembert. In Minkowski space, in standard coordinates (t, x, y, z), it has the form Here is the 3-dimensional Laplacian and ημν is the inverse Minkowski metric with , , for . (Some authors alternatively use the negative metric signature of (− + + +), with .)
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- D'Alembert's equation
- D'Alembert's principle
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- enIn special relativity, electromagnetism and wave theory, the d'Alembert operator (denoted by a box: ), also called the d'Alembertian, wave operator, box operator or sometimes quabla operator (cf. nabla symbol) is the Laplace operator of Minkowski space. The operator is named after French mathematician and physicist Jean le Rond d'Alembert. In Minkowski space, in standard coordinates (t, x, y, z), it has the form Here is the 3-dimensional Laplacian and ημν is the inverse Minkowski metric with , , for . Note that the μ and ν summation indices range from 0 to 3: see Einstein notation. We have assumed units such that the speed of light c = 1. (Some authors alternatively use the negative metric signature of (− + + +), with .) Lorentz transformations leave the Minkowski metric invariant, so the d'Alembertian yields a Lorentz scalar. The above coordinate expressions remain valid for the standard coordinates in every inertial frame.
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- 5457H
- D'Alembertiaan
- D'Alembertiano
- D'alembertien
- D'Alembert işleci
- D'Alembert operator
- D'Alembert-operatoren
- D'Alembertův operátor
- D’Alembert-Operator
- D’Alembertov operátor
- m.01qx9m
- Operador de d'Alembert
- Operador de d'Alembert
- Operator d’Alemberta
- Operatore di d'Alembert
- Operatoro de d'Alembert
- Q911268
- Д'Аламберов оператор
- Оператор Д’Аламбера
- Оператор д'Аламбера
- Оператор на Д'Аламбер
- ד'אלמברטיאן
- عملگر دالامبر
- ダランベール演算子
- 达朗贝尔算符
- 달랑베르 연산자
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- Category:Differential operators
- Category:Hyperbolic partial differential equations
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- enD'Alembert operator
- end'Alembertian
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