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?

  1. Mar 27, 2008 #1
    1. The problem statement, all variables and given/known data

    For a particle in the ground state of a rigid box, calculate the probability of finding it between x=0 and x=[tex]\frac{L}{3}[/tex]

    2. Relevant equations

    [tex]\left|\psi^{2}\right| = \frac{2}{L}Sin^{2}\left(\frac{nx\pi}{L}dx\right)[/tex]

    3. The attempt at a solution

    [tex]= \frac{2}{L}\int^{\frac{L}{3}}_{0} Sin^{2}\left(\frac{x\pi}{L}\right)[/tex]
    [tex]= \frac{2}{L}\int^{\frac{L}{3}}_{0} \frac{1-Cos \left(\frac{2x\pi}{L}\right)}{2}[/tex]

    [tex]\frac{1}{L} \int^{\frac{L}{3}}_{0} 1 - \int^{0}_{\frac{L}{3}} Cos \left(\frac{2x\pi}{L}\right)}[/tex]

    [tex]\frac{1}{L} \left[ \left|x\right|^{\frac{L}{3}}_{0} - \left|\frac{L}{2\pi}Sin\left(\frac{2x\pi}{L}\right)\right|^{\frac{L}{3}}_{0} [/tex]

    [tex]\frac{1}{L} \left[ \frac{L}{3}} - \frac{L}{2\pi}Sin\left(\frac{2\pi}{3}\right)\right] [/tex]

    factor out the L

    [tex]\frac{1}{3}} - \frac{1}{2\pi}Sin\left(\frac{2\pi}{3}\right)\right] [/tex]

    stuck here...when I work it out I get a negative number...am I mising something?
    Last edited: Mar 27, 2008
  2. jcsd
  3. Mar 27, 2008 #2


    User Avatar
    Gold Member

    [tex]\frac{1}{3}} - \frac{1}{2\pi}Sin\left(\frac{2\pi}{3}\right)\right] [/tex]

    I get a positive number -

    sin(2pi/3) = 0.8660

    0.8660/(2*pi ) = 0.1378

    1/3 - 0.1378 = 0.1955
  4. Mar 27, 2008 #3
    oh wow...stupid math mistake....forgot the parenthesis on my calc =(

    thank you!
  5. Jan 23, 2010 #4
    what would the probability of the particle be if x=1.95 and 2.05?
  6. Jan 23, 2010 #5
    the answer is supposed to be .007, but I keep getting -.2921
  7. Apr 19, 2011 #6
    I think you should be using cos instead of sin for the ground state.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook