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deedsy
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Homework Statement
I was hoping someone could verify that I've set up the integral correctly for this problem..
Suppose that at t=0, the wavefunction of a free particle is
[tex]ψ(x,0) = \sqrt{b} e^{-|x|b + ip_0 x/\hbar} [/tex]
a) what is the momentum amplitude for this wave function?
Homework Equations
*see below
The Attempt at a Solution
So, I think I know how to complete this, and just want to make sure I'm setting up the integral correctly before I dive into solving it.
a) I will use [tex]\phi(p,0)= \frac{1}{\sqrt{2\pi\hbar}}\int_∞^∞ ψ(x,0) e^{-ipx/\hbar}\,dx [/tex] ---> that's minus ∞ to ∞
so, for my wavefunction...
[tex]\phi(p,0)= \frac{1}{\sqrt{2\pi\hbar}}\int_\infty^\infty \sqrt{b} e^{-|x|b + ip_0 x/\hbar} e^{-ipx/\hbar}\,dx [/tex] ---> again, -∞ to ∞
Here, it looks like i can't cancel [itex]e^{ip_0 x/\hbar}[/itex] and [itex]e^{-ipx/\hbar} [/itex], and I'm stuck with what looks like a very nasty integral...
[tex]\phi(p,0)= \frac{1}{\sqrt{2\pi\hbar}}\int_\infty^\infty \sqrt{b} e^{-|x|b} e^{ix/\hbar (p_0-p)}\,dx [/tex] ---> again, -∞ to ∞
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