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Schrodinger Equations and Probability Density Functions

  1. May 17, 2009 #1
    1. The problem statement, all variables and given/known data
    A Particle is described by the normalized wave function
    psi(x,y,z) = Ae^(-alpha[x^2 + y^2 + z^2])
    Where A and alpha are real positive constants

    a)Determine the probability of finding the particle at a distance between r and r+dr from the origin
    hint: use the volume of the spherical shell centered on the origin with inner radius r and thickness dr.
    b) For what value of r does the probability in part a) have it's maximum value? Is this the same value of r for which |psi(x,y,z)|^2 is a maximum? explain any differences


    2. Relevant equations
    |psi(x)|^2 = 1


    3. The attempt at a solution

    Got no idea, like all 4 questions i'm posting any help would be appreciated, as i am completely lost
     
  2. jcsd
  3. May 19, 2009 #2

    malawi_glenn

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    Science Advisor
    Homework Helper

    the integration measure for sphere is r^2dr d(phi) d(cos theta)

    for a) just use the hint, take the probability of finding particle inside sphere with radius r + dr and substract with the probabilitiy to find it inside sphere with radius r.

    for b) you know how to find maxima of a given function right?
     
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