Let and write for the Cartesian space of dimension . Then a plane wave on is a function
given by the exponential function with complex argument of the form
Here is the wave vector of this plane wave (and is its amplitude).
In Fourier analysis over Cartesian space, the Fourier transform expresses every function with rapidly decreasing partial derivatives as a superposition of plane waves.
If here is identified with Minkowski spacetime with canonical coordinates labeled , then the 0-component of the wave vector
is called the frequency of the wave (in this chosen coordinate system). If in this situation the wave vector satisfies , then the plane wave is a solution to the wave equation on Minkowski spacetime. If more generally it satisfies for some , the it is a solution to the Klein-Gordon equation on Minkowski spacetime.
plane waves on Minkowski spacetime
See also
Last revised on August 2, 2018 at 07:10:53. See the history of this page for a list of all contributions to it.