Chapter 4.3, Problem 4.27P

(a)

To determine

Show that the allowed energies of the given rigid rotor are $E_n=\frac{{\hslash }^2}{2I}n\left(n+1\right)\left(n=0,1,2,\mathrm{...}\right)$ where $I=\frac{m_1{m}_2}{\left(m_1+m_2\right)}{a}^2$ is the moment of inertia of the system.

(b)

To determine

The normalized eigenfunction for the given system and the degeneracy of the $n^{th}$ energy level.

(c)

To determine

The spectrum that would be expected from the given system.

(d)

To determine

The frequency separation $\Delta \nu$ of carbon monoxide and the distance between the atoms $a$.