Vibrational energy level of a diatomic molecule

Vibrational energy level of a diatomic molecule is given by,

$$E_v = ( v + \frac{1}{2} ) \hbar \omega_0$$

Where, v=0,1,2,3…. is the vibrational quantum number, $$\omega_0 = \sqrt \frac{k}{\mu}$$ , $$\mu$$ is the reduced mass of the diatomic molecule and k is the force constant.

The selection rule for transition between vibrational states is,

$$\Delta v= \pm 1$$