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Calculate the probability that the electron is in the range

  1. Oct 19, 2004 #1
    Was just wondering if anyone could help me w/ this question.

    Consider the wave function
    (psi (x,t)) = (1/sqrt(2))[u2(x)exp(-iE2t/h(bar) + u3(x)exp(-iE3t/h(bar)}. calculate the probability that the electron is in the range (0,L/2) as as function of time. What is the period of oscillation of the probability? NOTE: the wavefuctions u2(x) and u3(x) refer to the n=2 and n=3 states of the infinite well located at 0<x<L.

    any help would be appreciated.
     
  2. jcsd
  3. Oct 19, 2004 #2

    Kane O'Donnell

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    Science Advisor

    I'm guessing that [tex]u_3(x)[/tex] is supposed to have a coefficient of [tex]\frac{1}{\sqrt{2}}[/tex] (so that the wavefunction is normalised).

    What you have to do is do calculate the probability integral for 0 < L < L/2. That is, do the integral from 0 < x < L/2 of [tex]\Psi^{*}\Psi[/tex]. You'll notice that the probability density [tex]\Psi^{*}\Psi[/tex] is no longer time-independent! It will wobble between being the u2 probability density and being the u3 probability density - figuring out the period of oscillation shouldn't be too hard once you have the density function sorted out.

    Cheerio!

    Kane
     
    Last edited: Oct 19, 2004
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