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Expectation value for a position measurement

  1. Dec 19, 2013 #1
    1. The problem statement, all variables and given/known data
    Given the wave function psi(x,0) = 3/5 sqrt(2/L) sin(xpi/L) + 4/5 sqrt(2/L) sin(5xpi/L) in an infinite potential well from 0 to L, what is the expectation value <x> and rms spread delta E = sqrt(<E^2>-<E>^2)


    2. Relevant equations
    <x> = integral from 0 to L of psi*xpsi dx


    3. The attempt at a solution
    I know that the expectation value <E> is just 3/5 E1 + 4/5 E2, however I'm not sure how to find the rms spread of it without cumbersome algebra. And the same with <x>.
     
  2. jcsd
  3. Dec 19, 2013 #2

    TSny

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    Homework Helper
    Gold Member

    Hello, SkyChaser.

    Your answer for <E> is not correct. Think about what you need to do to the coefficients 3/5 and 4/5 to get the probabilities.

    The algebra for the rms spread of E will be less cumbersome if you express E2 as a multiple of E1 and then express <E> and <E2> in terms of just E1.
     
  4. Dec 19, 2013 #3

    jtbell

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    Staff: Mentor

    I'm confused. Your title says "position measurement" but you refer to both x and E. To clarify, which one do you want: <x> or <E>? Δx or ΔE?
     
  5. Dec 19, 2013 #4
    Both. And yeah, it should be 9/25 E1 + 16/25 E2.
     
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