Wave vector
From Encyclopedia of Mathematics
The vector 
in the expression
 | (*) |
where 
and 
are constants and 
denotes time.
The usual physical interpretation of (*) is a plane wave of frequency 
, propagating in the direction of the vector 
and having wave-length 
, where 
. Many homogeneous linear equations and systems of partial differential equations (including the more important equations of mathematical physics such as the Maxwell equations and the wave equation) have solutions in the form (*).
Comments
References
| [a1] | F. John, "Plane waves and spherical means applied to partial differential equations" , Interscience (1955) |
| [a2] | I.M. Gel'fand, G.E. Shilov, "Generalized functions" , 1. Properties and operations , Acad. Press (1964) (Translated from Russian) |
How to Cite This Entry:
Wave vector. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Wave_vector&oldid=49177
Wave vector. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Wave_vector&oldid=49177
This article was adapted from an original article by V.M. Babich (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article