Diatomic molecule at a constant temperature

[LCSphysicist]

Homework Statement

All below...

Relevant Equations

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A diatomic molecule $D_{2}$ in $30K$, in $t=0$, is in the state $| \psi (0) \rangle = \frac{1}{\sqrt{26}}(3 | 1,1 \rangle + 4| 7,3 \rangle + | 7,1 \rangle )$, where the kets denote states $| l,m \rangle$. Use $\frac{\hbar}{Ic4\pi}=30.4cm^{-1}$.

Obtain $| \psi (t) \rangle$

I think the main point here is to deduce what is the Hamiltonian of the system. But i don't know waht could i use!

First i thought it could be a rotator, so $H = \frac{L^2}{2I}$. But doing so, i am not sure how the temperatura enters in the problem!

It seems that the probability should follows the canonical formalism, so $P \propto e^{-\beta E}$, where $P$ is the probability of the state with energy $E$. But how to connect it to a rotator?
(If the rotator idea is correct)

 

[DrClaude]

Without an explicit coupling to the environment, there is no way to solve this for the case of constant temperature.

As the molecule is in a pure state at $t=0$, I would continue treating it as an isolated system and disregard the mention of temperature.