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Changed the Hamiltonian after approximation to include H_0. If this is not correct, that is the original energies of ground state g and excited state e get shifted up by hbar omega_0/2 then the text should reflect upon that. The way the approximation is stated now however, it seems that we only need to exclude the exponential terms in H_1 - therefore H_0 remains unchanged. |
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Finally, transforming back into the [[Schrödinger picture]], the Hamiltonian is given by
:
H^\text{RWA}=\frac{\hbar\omega_0}{2}|\text{e}\rangle\langle\text{e}|-
\frac{\hbar\omega_0}{2}|\text{g}\rangle\langle\text{g}|
-\hbar\Omega e^{-i\omega_Lt}|\text{e}\rangle\langle\text{g}|
-\hbar\Omega^*e^{i\omega_Lt}|\text{g}\rangle\langle\text{e}|.
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