2. Construct a model for an electric dipole transition between two states that differ in energy by ℏΩ.
a. Derive the Heisenberg equation of motion for a complete set of operators (identity and Pauli operators).
b. Calculate the equation of motion of the expectation value of the dipole operator in the ground state (the initial state) for weak electric fields.
c. What is the consequence for the frequency-dependent polarizability?