Show that integral from - infinity to + infinity of psi_1(x) times psi_2*(x) dx is equal to integral from - infinity to + infinity of phi_1(k) times phi_2*(k) dk.
* indicates complex conjugate
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Problem: Show that
where [ ]* indicates complex conjugate.
This problem is related to the Fourier transform of a function or distribution.
First of all, we need to define the Fourier transform, since there are several ways to define this transform, although the properties are the same.
According to the statement to be proved, the Fourier transform of a function (x) will be defined as:
Its inverse is
The following posting helps with Fourier transform problems. Complex conjugates are indicated.