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This lecture covers the model Hamiltonian of Jaynes & Cummings, which describes the interaction between atoms and harmonic modes in a cavity. It explains the energy terms of the Hamiltonian for a two-level system coupled with a harmonic oscillator and an interaction term. The lecture also delves into the dynamics of spin in a magnetic field and the spectrum of eigenstates, emphasizing the coupling between two-level systems and harmonic modes.