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Crazy Tosser
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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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