# D'Alembert operator

wave operator, d'Alembertian

The second-order differential operator which in Cartesian coordinates assumes the following form:

where is the Laplace operator and is a constant. Its form in spherical coordinates is:

in cylindrical coordinates:

in general curvilinear coordinates:

where is the determinant of the matrix formed from the coefficients of the metric tensor .

Named after J. d'Alembert (1747), who considered its simplest form when solving the one-dimensional wave equation.