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fixed eq. for H_1^{RWA} |
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Now we apply the RWA by eliminating the counter-rotating terms as explained in the previous section, and finally transform the approximate Hamiltonian <math>H_{1,I}^{\text{RWA}}</math> back to the Schrödinger picture:
: <math>\begin{align}
H_1^{\text{RWA}}&=U^\dagger H_{1,I}^{\text{RWA}} U \\
&=-\hbar\Omega e^{-i\Delta t}e^{-i\omega_0t}|\text{e}\rangle\langle\text{g}|
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&=-\hbar\Omega e^{-i\omega_Lt}|\text{e}\rangle\langle\text{g}|
-\hbar\Omega^*e^{i\omega_Lt}|\text{g}\rangle\langle\text{e}|.
\end{align}</math>
The atomic Hamiltonian was unaffected by the approximation, so the total Hamiltonian in the Schrödinger picture under the rotating wave approximation is
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