Fourier integral / transform ? What is it really?

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Homework Help Overview

The discussion revolves around the application of Fourier transforms, specifically focusing on finding phi(k) and understanding the underlying principles of Fourier integrals. Participants are exploring the necessary steps and concepts involved in this mathematical context.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants are attempting to understand how to apply the Fourier transform to their problem, with one suggesting the use of integration techniques involving delta functions. Others are considering the method of completing the square in the exponential terms and questioning the simplification process.

Discussion Status

The discussion is active, with various approaches being suggested. Some participants are providing guidance on integration techniques, while others are exploring the implications of manipulating exponential terms. There is no explicit consensus yet, as different methods are being considered.

Contextual Notes

Participants are navigating the complexities of the Fourier transform and its application, indicating potential gaps in understanding or missing information regarding the problem setup.

student1938
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Find phi(k)

I need help with this question as far as what am I looking for and how do I use a Fourier transform cause I think I need one.

student
 

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Any suggestions guys?
 
Set t = 0, multiply both sides by
[tex]e^{-i k' x}[/tex]
and integrate over x. The integrand
[tex]e^{i(k-k')x}[/tex]
in the x integral will yield a delta function which let's you evaluate the k integral.
 
try completing the square in the exponential...
 
If i multiple both sides by exp(-ik'x) the LHS gives exp(-ik'x-(x/2a)^2). I' m not sure what to do with this to simplify it further. Do i have to try to complete the square in this exponential now?
 
student1938 said:
If i multiple both sides by exp(-ik'x) the LHS gives exp(-ik'x-(x/2a)^2). I' m not sure what to do with this to simplify it further. Do i have to try to complete the square in this exponential now?

Yes, that's what Dr T was suggesting.
 

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