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Question about expectation values.

  1. Dec 11, 2012 #1
    Is it possible to define operators to find the expectation value of position for a Gaussian wave packet. Similar to finding raising and lowering operators for the harmonic oscillator in terms of position and momentum and then using those to find <x> and <p>. But I was just wondering if this could be done for a Gaussian wave packet.
  2. jcsd
  3. Dec 11, 2012 #2


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    Staff: Mentor

    Here is one: X

    If your wave packet is expressed as function of position, ##<X> = \int \psi \psi^* x dx##.
  4. Dec 12, 2012 #3
    I don't completely understand what you are doing? Is X my new operator.
    are you starting with the definition of expectation value and then going from there.
  5. Dec 12, 2012 #4


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    The position operator (in the position representation) is simply ##x##. So the general definition of expectation value:

    $$\langle A \rangle = \int {\Psi^* A_{op} \Psi dx}$$


    $$\langle x \rangle = \int {\Psi^* x \Psi dx}$$

    Plug in your wave function and grind out the integral.
  6. Dec 13, 2012 #5
    ok i understand that. I was trying to think of a way to compute that with out doing an integral. Like how you can do that for the harmonic oscillator with a+ and a -
    like [itex] <x>=<U|a^+ + a^-|U> [/itex]
    u is the wave function and a+ is the raising operator.
    can I do this for a Gaussian wave packet.
  7. Dec 14, 2012 #6


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    If you define appropriate operators.
    For a gaussian wave packet, the expectation value of the position is the central value of the distribution. If you know that, you are done.
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