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as stated. The next step is to find the Hamiltonian in the [[interaction picture]], <math>H_{1,I}</math>. The required unitary transformation is
: <math>U = e^{iH_0t/\hbar} = e^{i \omega_0 t |\text{e}\rangle \langle\text{e}|} = |\text{g}\rangle \langle\text{g}| +e^{i \omega_0 t} |\text{e}\rangle \langle\text{e}|</math>,
where the last step can be seen to follow e.g. from a [[Taylor series]] expansion, and due to the orthogonality of the states <math>|\text{g}\rangle</math> and <math>|\text{e}\rangle</math> we have
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