According to the classical view of rotational spectroscopy the rotational motion of a molecule that has a dipole moment leads to an oscillating dipole moment. That oscillation is the origin of the transition dipole moment in this case. Radiation can interact with the dipole moment to cause it to absorb energy. In this case, the energy would be microwave energy.
Quantum view of rotational spectroscopy
The quantum view of rotation begins with the Schrodinger equation. There is no potential energy of rotation. The hamiltonian has the form of a second derivative of angular terms. The solution of the wave equation is a set of LeGendre polynomials, which are mathematically identical to the solutions of the angular part of the hydrogen atom. The reason for these identical solutions is that these are both problems with spherical symmetry. The wave functions that solve the angular equation are known as spherical harmonics. These are nothing more than standing waves on a sphere..
The transitions between quantum states follow a selection rule. The quantum number J can change by +1 or -1. Absorption of microwave radiation leads to a change of +1 and emission leads to a change of -1. The origin of this selection rule is similar to the other kinds of spectroscopy that we have studied. The microwave radiation that interacts with a rotating molecule has an angular momentum quantum number of 1. When the radiation is absorbed the angular momentum must move onto the rotating system in order to maintain conservation of angular momentum.
