Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

    mfb

    User Avatar
    2016 Award

    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

    jtbell

    User Avatar

    Staff: Mentor

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

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

    becomes

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

    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

    mfb

    User Avatar
    2016 Award

    Staff: Mentor

    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.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Question about expectation values.
  1. Expectation value (Replies: 5)

  2. Expectation Values (Replies: 1)

  3. Expectation value (Replies: 2)

Loading...