How to find the degeneracy of a given state in quantum mechanics? What is the formula?

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    $\begingroup$ Welcome to Chem.SE. It is a policy of the site that when posting a homework problem you should demonstrate your attempt to find a solution. $\endgroup$ – Buck Thorn Jan 26 '19 at 11:21
  • $\begingroup$ Sorry but I got my exams knocking on the door... It's a national level entrance exam for MSc, so I don't really have that much time to show the solution as well... really sorry... And it's not like I post a question without trying first. $\endgroup$ – user67074 Jan 27 '19 at 15:37

The energy is normally written as $\displaystyle E=\ell(\ell+1)\frac{\hbar^2}{2I}$ where $\ell$ is angular momentum and $I$ the moment of inertia. The multiplicity is $2\ell+1$ and in the absence of any perturbation this is the degeneracy. You can see that 9 is the correct answer if $\ell=4$

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