The function arises in various physical problems in describing electromagnetic response in complicated media.
* problems involving small-amplitude waves propagating through [[Maxwell–Boltzmann distribution|Maxwellian]] [[Plasma (physics)|plasmas]], and in particular appears in the plasma's [[permittivity]] from which [[dispersion relation]]s are derived, hence it is sometimes referred to as the '''plasma dispersion function<ref name=":0"lehtinen>{{Cite web|url=http://nlpc.stanford.edu/nleht/Science/reference/errorfun.pdf|title=Error functions|last=Lehtinen|first=Nikolai G.|date=April 23, 2010|website=Lehtinen webpage - Stanford University|url-status=live|archive-url=|archive-date=|access-date=October 8, 2019}}</ref>'''<ref name=Zaghloul11/> (although this name is sometimes used instead for the rescaled function <math>Z(z)=i\sqrt{\pi}w(z)</math> defined by ''Fried and Conte'', 1960<ref name=":0"lehtinen /><ref>[http://farside.ph.utexas.edu/ Richard Fitzpatrick], [http://farside.ph.utexas.edu/teaching/plasma/lectures/node87.html Plasma Dispersion Function], ''[http://farside.ph.utexas.edu/teaching/plasma/plasma.html Plasma Physics]'' lecture notes, University of Texas at Austin (2011/3/31).</ref>).
* the infrared [[permittivity]] functions of amorphous oxides have resonances (due to [[phonon]]s) that are sometimes too complicated to fit using simple harmonic oscillators. The Brendel–BormanBrendel–Bormann oscillator form uses an infinite superposition of oscillators having slightly different frequencies, with a Gaussian distribution.<ref name="BrendelBormann1992">{{cite journal|last1=Brendel|first1=R.|last2=Bormann|first2=D.|title=An infrared dielectric function model for amorphous solids|journal=Journal of Applied Physics|volume=71|issue=1|year=1992|pages=1|issn=0021-8979|doi=10.1063/1.350737|bibcode=1992JAP....71....1B}}</ref> The integrated response can be written in terms of the Faddeeva function.
* the Faddeeva function is also used in the analysis of electromagnetic waves of the type used in AM radio.{{citation needed|date=July 2016}} Groundwaves are verticaly polarised waves propagating over a lossy ground with finite resistivity and permittivity.
