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: Particle in a box

  1. Jun 19, 2010 #1
    1. The problem statement, all variables and given/known data

    A particle is moving in a one dimensional box of infinite height of width 10 Angstroms. Calculate the probability of finding the particle within an interval of 1 Angstrom at the centre of the box, when it is in its state of least energy.

    2. Relevant equations

    \psi _{n}=\sqrt{\frac{2}{L}}sin \frac{n\pi x}{L}

    3. The attempt at a solution
    The wave function of the particle in the ground state (n=1) is [tex]\psi _{1}=\sqrt{\frac{2}{L}}sin \frac{\pi x}{L}[/tex]. Now, what should I do ?
  2. jcsd
  3. Jun 19, 2010 #2
    How does one find the probability amplitude in QM?
  4. Jun 19, 2010 #3
    Square of its wavefunction. I got <tex> \frac{2}{L}sin^2 \frac{\pi x}{L}</tex> Now...........
  5. Jun 19, 2010 #4
    Okay, now how do you find the probability on the interval [4 Angstroms,6 Angstroms]?
  6. Jun 19, 2010 #5
    Why between 4 and 6 angstroms ?
  7. Jun 19, 2010 #6
    [STRIKE]Why do you think it's between 4 and 6 angstroms?
    EDIT: Err rather I believe it should be from 4.5 to 5.5 angstroms...
  8. Jun 20, 2010 #7
    probability of finding the particle between x & x+dx is [tex]{|\Psi|}^{2}[/tex]

    probability of finding the particle between x=a and a=b is [tex]\int_{a}^{b}{|\Psi|}^{2}dx[/tex]
  9. Jun 20, 2010 #8
    What are the limits I should use for the integration?
  10. Jun 22, 2010 #9
    Find a and b for "an interval of 1 Angstrom at the centre of the box".
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook