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Computing Heisenberg Uncertainty Value

  1. Dec 17, 2011 #1
    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.
    Last edited: Dec 18, 2011
  2. jcsd
  3. Dec 18, 2011 #2


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    Homework Helper

    This is just integration not QM. But you first step is to use a trig identity sin(u)^2=(1-cos(2u))/2 to get rid of the power on the sin. Now multiply it out and start using integration by parts to deal with the x^2*cos part. You must have seen these things somewhere before.
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