Free wave equation: Difference between revisions

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The '''free wave equation''' on <math>R^{1+d}</math> is given by
The '''free wave equation''' on <math>{\mathbb R}^{1+d}</math> is given by
<center><math>\Box f = 0</math></center>
<center><math>\Box f = 0</math></center>
where ''f'' is a scalar or vector field on [[Minkowski space]] <math>R^{1+d}</math>.
where ''f'' is a scalar or vector field on [[Minkowski space]] <math>{\mathbb R}^{1+d}</math>.
In coordinates, this becomes
In coordinates, this becomes
<center><math>- \partial_{tt} f + \Delta f = 0.</math></center>
<center><math>- \partial_{tt} f + \Delta f = 0.</math></center>

Revision as of 14:38, 20 June 2009

The free wave equation on is given by

where f is a scalar or vector field on Minkowski space . In coordinates, this becomes

It is the prototype for many nonlinear wave equations.

One can add a mass term to create the Klein-Gordon equation.