Rotational properties of the harmonic oscillator

[DielsAlder]

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.

Homework Statement

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 dependence of the expectation value of B on the quantum number $\upsilon$ and other parameters.

Homework Equations

http://img36.imageshack.us/img36/3463/physicsforum1.jpg

The Attempt at a Solution

http://img189.imageshack.us/img189/1899/physicsforum2.jpg


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.

 

[DielsAlder]

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.