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m (Changed the eigenvalue variable to k^2 to be consistent with what follows. The previous use of \lambda is confusing, as this is the wavelength symbol for light waves, and is the inverse of the wavenumber) 
m 

This equation has important applications in the science of [[optics]], where it provides solutions that describe the propagation of [[electromagnetic waves]] (light) in the form of either [[parabolaparaboloidal]] waves or [[Gaussian beam]]s. Most [[laser]]s emit beams that take this form.
The assumption under which the paraxial approximation is valid is that the ''z'' derivative of the amplitude function ''u'' is a slowly
:<math> \bigg { \partial^2 u \over \partial z^2 } \bigg \ll \bigg { k {\partial u \over \partial z} } \bigg .</math>
