Can someone explain Fourier transform to me?

[Crazy Tosser]

OK< I've been trying to understands Fourier Transforms with no success. Does anybody know a tutorial or website that explains it completely? My math background is Calculus AB, and my Physics background is reg. physics, but I am into QM, and already know basic wave equations and can apply Heisenberg's uncertainity Principle.

There is this problem that I want to solve:

Homework Statement

Consider the wave packet $$cos(\alpha x) e^{- \beta |x|}$$, where $$\alpha$$ and $$\beta$$ are real positive constants and $$\beta << \alpha$$. Take the Fourier transform of this expression and show that the frequency components are spread over a range $$\Delta k \approx \beta$$. Thus, deduce the uncertainty relation.

Homework Equations

$$\Delta x \Delta p \approx h$$
$$\Delta k \approx \frac{1}{\Delta x}$$
and probably the Fourier transform equation that I don't remeber right now.

The Attempt at a Solution

$$\Delta k \approx \frac{1}{\Delta x}$$, thus $$\Delta k \approx \frac{\Delta p}{h}$$, thus $$\Delta k \approx \frac{\Delta v}{c}$$

If it's right, where do I go from here?
How can I use the Fourier transforms here?

 

[malawi_glenn]

have you tried wikipedia?

 

[Crazy Tosser]

Yes, and could not understand any damn thing

 

[pam]

There are many math physics books in the library.

 

[Redbelly98]

Homework Equations

$$\Delta x \Delta p \approx h$$
$$\Delta k \approx \frac{1}{\Delta x}$$
and probably the Fourier transform equation that I don't remeber right now.

The Fourier transform equation is the key, and should be in your textbook or class notes. You'll have to do the integral.

 

[malawi_glenn]

Yes, and could not understand any damn thing

It is basically just 'doing an integral'.

It is easier if you tell us exactly what it is that you don't understand, then we can help you with that.

 

[siddharth]

Also, I'll repeat what pam said, and suggest that you go to any library and get a book. This is true for any subject in general. You'll learn much more from going to the library and getting a book, instead of asking on an online forum, because it is almost impossible to explain subjects completely. http://mathworld.wolfram.com/FourierTransform.html" has many references. As malawi said, if you have any *specific* questions, post them here and you'll get help.

I recommend "A Student's Guide to Fourier Transforms: With Applications in Physics and Engineering" by J.F James. It's a small book, but very well written.