The discussion revolves around the Fourier transform of the sine function, specifically addressing the complexities that arise when considering non-zero terms. Participants are examining the implications of using complex exponentials in the transformation process.
The discussion is active, with participants exploring various interpretations of the transformation and its components. Some have pointed out potential errors in the integration process, while others are seeking clarification on the implications of these errors.
There seems to be a focus on the correctness of the primitive function for specific values of k, particularly k = 1, and how this affects the overall transformation. Participants are also addressing the role of real and imaginary parts in the context of the Fourier transform.
Indeed, but more importantly it should also be realised that the primitive function is incorrect for ##k = 1##.anuttarasammyak said:
Ohh alright yeah that makes sense. Ty!anuttarasammyak said:
What does this mean?Orodruin said:
That your integration is wrong when k = 1.lys04 said:
It's gonna be wrong for all k s.t e_-ikx has a real part?Orodruin said:
You are misunderstanding my comment. I said that apart from the fact pointed out by @anuttarasammyak in post #2, the integral is also wrong for ##k = 1##. This will be crucial to correct also when you have corrected the imaginary part error.lys04 said:
(my emphasis)Orodruin said: