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For the infinite well: $$U(x)=\quad\infty : x \leq 0\quad 0 : 0 < x < L\quad \infty : x \geq L$$

$\psi_n=$$\sqrt{\frac{2}{L}}\sin{\frac{n\pi x}{L}}$

Find $\Delta x_n$, the uncertainty in position for some arbitrary eigenstate psi.n

So the attempt I made at doing this was to find using $\Delta x_n=\sqrt{<x^2>-<x>^2}$ I went through and found $$<x^2>=L^2(\frac{1}{3}-\frac{1}{2\pi^2})$$ and $$<x>^2=\frac{L^2}{4}$$ This led to the final result of $$L\sqrt{\frac{2\pi^2-12}{24\pi^2}}$$ When I went on to the next part of the question and found $\Delta p_n=\frac{\pi\hbar}{L}$ and then used this with $\Delta x_n$ to verify the uncertainty principle, I failed.

What have I done incorrectly, I can't see it. I used my book to verify the integrals.

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Your question would be much easier to understand if you use latex notation for math. –  fffred Nov 1 '13 at 0:06

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