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Expectation value

  1. Dec 6, 2005 #1
    how do you find the expectation value <x> for the 1st 2 states of a harmonic oscillator?
  2. jcsd
  3. Dec 6, 2005 #2
    The expectation value of an operator A is <psi|A|psi>. If you're not familiar with Dirac's notation that means that for state 1 you'd integrate psi1 times A times psi1 over all space.

    Once you start getting your hands dirty with the integrations pay attention to wether the integrand is even or odd. That will save you from a lot of useless intergration. Also the gamma function may prove to be useful.
  4. Dec 6, 2005 #3


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    Well, they are [itex]\langle \psi_0|x|\psi_0\rangle[/itex] and [itex]\langle \psi_1|x|\psi_1\rangle[/itex] ofcourse.
    You could find them either by integration or the application of the ladder operators.

    However, a look at the probability distributions [itex]|\psi_0|^2[/itex] and [itex]|\psi_1|^2[/itex] should tell you immediately what the expectation value for the position is.
  5. Dec 6, 2005 #4
    You can do that, but if you really want to see the math, use the ladder operators.

    - harsh
  6. Dec 8, 2005 #5
    ladder operators? what's that?
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