(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

I have to find the hamiltonian for a diatomic molecule, where the molecule can only rotate and translate and we supose that potencial energy doesn't change.

2. Relevant equations

3. The attempt at a solution

Okey so I used Spherical coordinate system such as the kinetic energy of the molecule is

[tex]T=\frac{1}{2}(m\dot{r}^2+I(\dot{\phi}^2+I(\dot{θ})^2)=L[/tex]

To find the Hamiltonian i've considered:

[tex]P_r=m\dot{r} \Rightarrow \dot{r}=\frac{P_r}{m}[/tex]

And so on for the other momentum so the final solution for the hamiltonian is:

[tex]H=\frac{1}{2}(\frac{P_r^2}{m}+\frac{P_\phi^2}{I}+ \frac{P_θ^2}{I})[/tex]

BUT the correct solution given by my professor is:

[tex]H=\frac{1}{2}(\frac{P_r^2}{m}+\frac{P_\phi^2}{I \sin^2\theta}+ \frac{P_θ^2}{I})[/tex]

So I don't know why is there a sin^2\theta factor.

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# Homework Help: Diatomic molecule Hamiltonian

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