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Homework Help: Harmonic Oscillator

  1. Dec 18, 2013 #1
    1. The problem statement, all variables and given/known data

    I need to show that for an eigen state of 1D harmonic oscillator the expectation values of the position X is Zero.

    2. Relevant equations



    3. The attempt at a solution

  2. jcsd
  3. Dec 18, 2013 #2


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    Staff: Mentor

    That doens't look like the standard form, see http://en.wikipedia.org/wiki/Quantum_harmonic_oscillator#Ladder_operator_method

    You won't get ##\hat{x}## from ##a^+ + a^-## with those.

    What is your question exactly? Can you figure out what
    \left( a^- + a^+ \right) \left|n\right\rangle
    results in?
  4. Dec 19, 2013 #3
    I used the book "Fundamentals of Quantum Mechanics for Solid State Electronics Optics" - C.Tang
    Here is the link to the book :http://en.bookfi.org/book/1308543 [Broken] (page 79 (pdf)).

    Using the a+ and a- in the link you gave I get:

    Now using:

    I get:

    Now can I say that since all {n} vectors are orthogonal the expression<n|[itex]\sqrt{n+1}[/itex]|n+1>=[itex]\sqrt{n+1}[/itex]<n|n+1>=0?

    Last edited by a moderator: May 6, 2017
  5. Dec 19, 2013 #4


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    Staff Emeritus
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    Yes, you can.
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