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Rabi Hamiltonian in the presence of a dc magnetic field

Consider first the Hamiltonian $H_0= \frac 12 \hbar \omega_0 \sigma_z$. The eigenvalues are $\pm \frac 12 \hbar \omega_0$ and the eigenvectors $|\uparrow:z\rangle,|\downarrow:z\rangle$. Now, before ...
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