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Rotational properties of the harmonic oscillator

  1. Dec 4, 2011 #1
    Hi everybody,

    This is my first post in this forum although I started following it some time ago. My question is related to rotational properties involving harmonic oscillator model.

    1. The problem statement, all variables and given/known data

    We are told to evaluate the expectation value of the rotational constant of a diatomic molecule for each vibrational state considering the Harmonic Oscillator model. I have started with the ground vibrational state, but the entire solution of the problem should include an expression for the dependance of the expectation value of B on the quantum number [itex]\upsilon[/itex] and other parameters.

    2. Relevant equations

    http://img36.imageshack.us/img36/3463/physicsforum1.jpg [Broken]

    3. The attempt at a solution

    http://img189.imageshack.us/img189/1899/physicsforum2.jpg [Broken]


    Do you agree with the way I am solving the problem? I don´t find the last gaussian-like definite integral in any of the tables I have consulted and I cannot find the solution by myself. Could you make me a suggestion about it?

    Thanks in advance.
     
    Last edited by a moderator: May 5, 2017
  2. jcsd
  3. Dec 8, 2011 #2
    Hi again,

    I have checked plenty of books about rotational spectroscopy but none of them include a detailed explanation about this topic. They only mention that even for harmonic oscillator the expectation value of 1/R^2 varies with the vibrational state.

    I am starting thinking that there may exist a different approach to the problem than solving the definite integrals I have proposed in the previous post.
     
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