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For simplicity consider a [[two-state quantum system|two-level atomic system]] with [[ground state|ground]] and [[excited state|excited]] states <math>|\text{g}\rangle</math> and <math>|\text{e}\rangle</math>, respectively (using the [[bra–ket notation|Dirac bracket notation]]). Let the energy difference between the states be <math>\hbar\omega_0</math> so that <math>\omega_0</math> is the transition frequency of the system. Then the unperturbed [[Hamiltonian (quantum mechanics)|Hamiltonian]] of the atom can be written as
: <math>H_0=\frac{\hbar\omega_0}{2}|\text{e}\rangle\langle\text{e}-|\frac{\hbar\omega_0}{2}|\text{g}\rangle\langle\text{g}|</math>.
Suppose the atom experiences an external classical [[electric field]] of frequency <math>\omega_L</math>, given by
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