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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

    [tex]
    \psi _{n}=\sqrt{\frac{2}{L}}sin \frac{n\pi x}{L}
    [/tex]

    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?
    [/STRIKE]
    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".
     
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