Â Equivalent to the divergence of the gradient, this operator may be best known for its appearance in the heat equation, a generalization of its namesake's partial differential equation.
One extension of this function to pseudo-Riemannian manifolds is the sum of the codifferential of an exterior derivative plus the exterior derivative of the codifferential. That operator is often co-named with de Rham or Beltrami. It appears in Poisson's equation, which explains why this operator acting on potential is equal to negative charge density over the permittivity of free space. The inclusion of a time differential generalizes this to the (*) d'Alembertian in Minkowski spaces. The kinetic energy operator, appearing in the Hamiltonian, is equivalent to negative h-bar squared over twice mass times this operator. Â Equivalent to the divergence of the gradient, this operator may be best known for its appearance in the heat equation, a generalization of its namesake's partial differential equation. For 10 points, name this operator typically symbolized by a del-squared or delta and named for a French mathematician.
One extension of this function to pseudo-Riemannian manifolds is the sum of the codifferential of an exterior derivative plus the exterior derivative of the codifferential.
Laplacian