Laplace operator

In mathematics and physics, the Laplace operator or Laplacian, denoted by Δ, is a differential operator, specifically an important case of an elliptic operator (or a hyperbolic operator, when defined on pseudo-Riemannian manifolds), with many applications in mathematics and physics. In physics, it is used in modeling of wave propagation and heat flow, forming the Helmholtz equation. It is central in electrostatics, anchoring in Laplace's equation and Poisson's equation. In quantum mechanics, it represents the kinetic energy term of the Schrödinger equation. In mathematics, functions with vanishing Laplacian are called harmonic functions; the Laplacian is at the core of Hodge theory and the results of de Rham cohomology.

Related Topics:
Mathematics - Physics - Differential operator - Elliptic operator - Hyperbolic operator - Pseudo-Riemannian manifold - Modeling - Wave propagation - Heat flow - Helmholtz equation - Electrostatics - Laplace's equation - Poisson's equation - Quantum mechanics - Kinetic energy - Schrödinger equation - Functions - Harmonic function - Hodge theory - De Rham cohomology

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