Integration question re Fourier Transform

1. Nov 30, 2004

celal777

Hello Listmembers,

I am trying to make some progress in my understanding of
Schrodinger's equation.I have been trying to teach myself about
Fourier transforms in the hope that this will help me understand the
derivation of Schrodinger's equation.

My question has to do with slide number 16 from a presentation which can be found at :

http://www.physics.gatech.edu/gcuo/UltrafastOptics/3803/OpticsI14FourierTransformI.ppt

My question is : I know about integrating the product of two
functions [see Section 6.1 at
http://mathews.ecs.fullerton.edu/c2002/ca0601.html] but i don't see
how you do end up with an expression containing "e" [i.e. the "exp"
factor] by performing integrations on the fourier coefficients above
it which contain sine and cosine functions ?

Sincerely
Celal Berker
London, England

Last edited by a moderator: Apr 21, 2017
2. Nov 30, 2004

Justin Lazear

Maybe I'm reading too quickly (or probably not at all), but that just looks like an application of the complex exponential.

$$e^{-i \theta} = \cos{\theta} - i\sin{\theta}$$

--J