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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:

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

[tex]\Delta x \Delta p \approx h[/tex]

[tex]\Delta k \approx \frac{1}{\Delta x}[/tex]

and probably the fourier transform equation that I don't remeber right now.

[tex]\Delta k \approx \frac{1}{\Delta x}[/tex], thus [tex]\Delta k \approx \frac{\Delta p}{h}[/tex], thus [tex]\Delta k \approx \frac{\Delta v}{c}[/tex]

If it's right, where do I go from here?

How can I use the Fourier transforms here?

There is this problem that I want to solve:

## Homework Statement

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

## Homework Equations

[tex]\Delta x \Delta p \approx h[/tex]

[tex]\Delta k \approx \frac{1}{\Delta x}[/tex]

and probably the fourier transform equation that I don't remeber right now.

## The Attempt at a Solution

[tex]\Delta k \approx \frac{1}{\Delta x}[/tex], thus [tex]\Delta k \approx \frac{\Delta p}{h}[/tex], thus [tex]\Delta k \approx \frac{\Delta v}{c}[/tex]

If it's right, where do I go from here?

How can I use the Fourier transforms here?

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