This chapter presents the basic elements of quantum theory, including the Dirac bra and ket notation for quantum states, Hermitian operators and their eigenstates, commutators and the Schrödinger and Heisenberg equations of motion. Simple model atoms are described as an effective spin and their properties related to the familiar Pauli spin-half operators. The density matrix is introduced to describe incoherent processes. The electric-dipole coupling between and atom and the electromagnetic field is treated leading to coupled equations for the probability amplitudes. Finally, quantized field modes are introduced and their elementary properties described leading to the fundamental Jaynes–Cummings model of a single two-state atom interacting with a quantized field mode.
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