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Help! Beginner Quantum Mechanics

  1. Jan 28, 2010 #1
    1. The problem statement, all variables and given/known data
    a particle is described by the normalized wave function
    [tex] \psi(x,y,z) = Axe^{-\alpha x^2}e^{-\beta y^2}e^{-\gamma z^2}[/tex]
    Where all constants are positive and real. The probability that the particle will be found in the infinitesimal volume dxdydz centered at point [tex] (x_{0},y_{0},z_{0}) [/tex] is [tex] \mid \psi (x_{0},y_{0},z_{0}) \mid ^2 dxdydz [/tex]

    a) at what values of [tex] x_{0} [/tex] is the particle most likely to be found
    b) are there any values of x for which the probability of the particle being found is zero?explain


    2. Relevant equations
    Alright so Im a newb when it comes to QM because we're just learning it now, I'm very confused with this question because it asks for probability of x when its over a region of x,y and z. Is it possible to use this [tex] \int \mid \psi (x_{0},y_{0},z_{0}) \mid ^2 dxdydz [/tex] and integrate over all space?? please can someone tell me where to start
     
  2. jcsd
  3. Jan 28, 2010 #2
    The question is kind of poorly worded. If you integrate |psi|^2 over all space, you should get 1 (the probability of finding the particle anywhere is 1), and that lets you fix the constant A in terms of alpha, beta and gamma. What they probably mean by (a) is: for a fixed value of y and z, the neighborhood around what value of x maximizes your probability of finding the particle? In (b), they mean the same sort of thing: are there any regions of space where the particle won't be?
     
  4. Jan 28, 2010 #3
    ok, but I still don't understand what to do...please someone just tell me where to start i'd really appreciate it this is frustrating me so much
     
  5. Jan 28, 2010 #4
    For what value(s) of x is |psi|^2 at a maximum? For what value(s) of x is |psi|^2 0?
     
  6. Jan 28, 2010 #5

    vela

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    As chrispb noted, the question is a bit ambiguous. What I think they want you do to is find the marginal probability density px(x) and find where it's a maximum and where it's zero. To find px(x), you integrate over y and z, so you're just left with x as a variable.

    chrispb suggested the other way to interpret the question. It turns out you'll get the same answer either way because of the wave function you have.
     
  7. Jan 28, 2010 #6
    oh ok, so i integrate over all space for y and z then I'm left with x and just solve for it then? i'll give er a try
     
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