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Expectation Velues

  1. May 1, 2009 #1
    Every quantum mechanical operator has an observable in classical mechanics

    <x> - position
    ...
    <x^2> - ?
    <p^2> - ?

    What is the meaning on these expectation values?

    v^2 = <x^2> - <x>^2

    What is the meaning of this? edit: It looks to me like uncertainty in position. Is it the average uncertainty in position?

    Admin Please move me to the right forum, if i'm not in eet.
     
  2. jcsd
  3. May 1, 2009 #2

    jtbell

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    Staff: Mentor

    This is the square of the uncertainty in position. That is,

    [tex]\Delta x = \sqrt {<x^2> - <x>^2}[/tex]
     
  4. May 1, 2009 #3
    That's what i figures too after some digging in the kinetics section of my chem book

    cheers.

    i still don't get what <x^2> means. What i found was "the average of the square of molecular speeds" but i still don't entirely get why its operator is X^2.

    edit: Also is there a ways to represent it geometrically or graphically
     
  5. May 1, 2009 #4

    jtbell

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    Staff: Mentor

    It's simply the average value of the square of the position, in the limit as the number of measurements goes to infinity. If you have N measurements of the position, then

    [tex]<x^2> = \frac{1}{N} \sum_{i=1}^N {x_i^2}[/tex]

    Actually this is only an approximation. It becomes exact as [itex]N \rightarrow \infty[/itex].

    The "average of the square of molecular speeds" would be [itex]<v^2>[/itex], calculated similarly, but with v replacing x.
     
  6. May 1, 2009 #5
    i get it now.

    thanks.
     
    Last edited: May 1, 2009
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