Rotation of diatomic molecules

Apply the spherical model to the rotation of diatomic molecules and to electron and nuclear spin... 

To no surprise, substitution of Equation 8-3 into Equation 8-1 along with operation of on Y/ (6, ( )) and subsequent cancellation of Y (6, ( )) results in the same two-body radial Schroedinger equation as previously obtained for the vibration/rotation of diatomic molecules with a general expression for the potential V(r) (see Equation 6-10). 

In the case of the vibration/rotation of a diatomic molecule, the /(/ -t 1) term in the radial Schroedinger equation is approximated via a power series expansion (see Equation 6-18). This approximation is sufficient for vibration/rotation of diatomic molecules because the distance of separation of the two nuclei does not vary greatly between rotational states. In the case of electronic states however, the separation of the electron and the nucleus varies widely between states and a power series expansion is inappropriate. Eortunately, the solution to Equation 8-6 is well known. There are an infinite number of solutions for each value of / and each one is designated by a quantum number n. Each state is called an atomic orbital (AO). The quantum numbers that distinguish the possible states is given as follows. 

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