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Wavefunction with specific values

  1. Nov 12, 2013 #1
    1. The problem statement, all variables and given/known data
    Near a certain position xA, a quanton's wavefunction ψ(xA)=-0.3 in some units. Near a certain position xB, a quanton's wavefunction ψ(xB[\SUB])=0.12 in the same units. If we do an experiment to locate the quanton, how many times more likely is i that the result is in a small range near xA than in a range twice as large near xB? Please explain.


    2. Relevant equations
    ψ(x)=ψ/sqrt(Δx)
    |ψ|2=Pr(x)


    3. The attempt at a solution
    I used the definitions of wavefunction and amplitude to get Pr(x)=|ψ(x)|2Δx.
    So Pr(xA)=(-0.3)2=0.09
    And Pr(xB)=2(0.12)2=0.0288
    Therefore Pr(xA)=3.125Pr(xB)

    Is this the right way to think about this? And how would I "explain"?
     
  2. jcsd
  3. Nov 12, 2013 #2

    ehild

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    Homework Helper
    Gold Member



    |ψ(x)|^2 is the probability density of finding the particle around some specified x. So the probability that a particle is in a narrow range of width Δx around x is P = |ψ(x)|^2 Δx.
    So P(xA) = Δx(-0.3)2=0.09 Δx and Pr(xB)=2Δx(0.12)2=0.0288 Δx, but you got the ratio correctly.

    ehild
     
    Last edited: Nov 12, 2013
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