1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Show that the expectation value of momentum is zero

  1. Apr 29, 2015 #1
    1. The problem statement, all variables and given/known data
    Demonstrate that the expectation value of momentum (p) for the wave function: ψ(x)∝e^(-γx) when x>0, ψ(x)=0 when x<0. Hint: Pay special attention to the discontinuity at x=0.


    2. Relevant equations
    <p>=<ψ|p|ψ>=∫dxψ*(x)[-iħ∂/∂x]ψ(x) from -∞ to ∞.



    3. The attempt at a solution
    I have normalized the wave function such that ∫ψ*(x)ψ(x)dx from -∞ to ∞ =1. I get a constant of √(2γ) so that ψ(x)=√(2γ)e^(-γx).

    Then, I attempt to set up the <p> integral as:
    <p>=∫√(2γ)e^(-γx)[iħ∂/∂x]√(2γ)e^(-γx)dx from -∞ to ∞.
    Simplifying, I get that the integral is: ∫2iħγ^2e^(-2γx)dx from 0 to ∞.
    I am fairly confident in my evaluation of this integral (which i get to be γiħ), but I do not know how to approach the discontinuity at x=0. I attempted to use a delta function, but I cannot seem to get the overall expectation value to equal 0.

    Thanks for any and all suggestions!
     
  2. jcsd
  3. Apr 29, 2015 #2

    mfb

    User Avatar
    2016 Award

    Staff: Mentor

    I think you could replace it by some smooth function that connects both parts, and then take the limit of zero width for this smooth function.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Show that the expectation value of momentum is zero
Loading...