Fourier integral / transform ? What is it really?

[student1938]

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

 

[student1938]

Any suggestions guys?

 

[Tide]

Set t = 0, multiply both sides by
e^{-i k' x}
and integrate over x. The integrand
e^{i(k-k')x}
in the x integral will yield a delta function which let's you evaluate the k integral.

 

[Dr Transport]

try completing the square in the exponential...

 

[student1938]

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?

 

[Tide]

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.