Thread: Landau Level Broadening View Single Post
P: 1
 Quote by Muneer QAU i read that real and imaginary parts of a complex number can be separated by following equation 1/x+iη=P(1/x)-iδ(x) where P is principal of x i dunt understand this equation can any 1 explain this?????????

the simplest example is if you have
\int \frac{f(x)}{\text{i$\epsilon$}+x} \, dx

so sometimes it is usefull to rewrite it in way
\int \frac{f(x)}{\text{i$\epsilon$}+x} \, dx=P \int \frac{f(x)}{x} \, dx-i \pi f(x)

where P means that you integrate in terms of principal value