# Faulty Uncertainty Calculations for a Ground State Particle in an Infinite Well

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.

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