(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Consider a particle in a one dimensional box of length L, whose potential energy is V(x)=0 for 0<x<L, and infinite otherwise.Given the wave function at ground state ψ=sqrt(2/L)sin (pi*x/L) Compute ΔxΔp where

2. Relevant equations

Δx=sqrt(<x^2>-<x>^2) and Δp=sqrt(<p^2>-<p>^2)

3. The attempt at a solution

I have set the expected value for as <x^2> equal to the integral from 0 to L ψ1(x)(x^2)ψ1(x)dx, as done by my prof. I then evaluated this to 2/L*the integral from 0 to L x^2sin^2(pi*x/L)dx. However I am stuck here, and my prof's solution goes straight to L^2(1/3-1/2pi^2). I am confused as to how he evaluated this integral and the role of (x^2) in the equation, if steps could be shown that would help immensely, also when calculating <x>, is x included in the integral, and how might it be evaluated if included with sin^2(pi*x/L). Thanks in advance.

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# Homework Help: Computing Heisenberg Uncertainty Value

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