1. Limited time only! Sign up for a free 30min personal 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!

Homework Help: Probability of finding a particle in a 1D Box

  1. Feb 1, 2010 #1
    1. The problem statement, all variables and given/known data

    Determine the probability of finding a particle in a 1-D box of size L in a region of size 0.01L at the locations x = 0, 0.25L, 0.5L, 0.75L and L when it is in its ground state. As percentages

    2. Relevant equations


    3. The attempt at a solution

    I'm not even sure if i've got the right equations there, i've tried loads of different ways of doing this and cannot get the right answers, which are 0%,1%,2%,1%,0%

  2. jcsd
  3. Feb 1, 2010 #2
    ok, finding probabilities means integrating the probability density - P=|[tex]\Psi[/tex](x,t)^2| - over parts of the box

    try integrating over the whole box first, what does this give you?...
  4. Feb 1, 2010 #3
    [tex]\int[/tex]|[tex]\Psi[/tex](x,t)^2| = |[tex]\Psi[/tex](x,t)^3| /3

    I think that's right.
    Last edited: Feb 1, 2010
  5. Feb 1, 2010 #4
    Your answer cannot be a function of x, since you are integrating over x. Try substituting your expression for [itex] \Psi(x) [/itex] from your first post before you integrate.
  6. Feb 1, 2010 #5
    You need to integrate |psi^2| from x=0 to x=0.01L , from x=0.245L to 0.255L, etc

    Try to plot psi, |psi^2| and the integral of |psi^2| from 0 to x (remember that the integral is the probabilty of finding the particle in the limits of integration...)
  7. Feb 1, 2010 #6
    Thanks guys, got a bit of extra help and the penny has dropped now. cheers
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook