Everything about Kramers-kronig Relations totally explained
The Kramers-Kronig relations are mathematical properties which connect the
real and
imaginary parts of any complex function
analytic in the upper half plane. These relations are often used to relate the real and imaginary parts of
response functions in physical systems because causality implies the analyticity condition is satisfied and conversely. The relation is named in honor of
Ralph Kronig and
Hendrik Anthony Kramers.
Definition
For a function
analytic in the upper half plane which vanishes as
, the Kramers-Kronig relations are given by
» .
These are the Kramers-Kronig relations useful for physical response functions.
Further Information
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