Homework Statement
The JCM has the Hamiltonian:
\hat{H} = \hbar \omega \left(\hat{a}\hat{a}^{*} + 1/2 \right) + \frac{\hbar\omega_{0}\hat{\sigma}_{z}}{2} + \hbar g (\hat{\sigma}_{+}\hat{a} + \hat{\sigma}_{-}\hat{a}^{*}
Find the eigenstates and energy eigenvalues in this non-resonant case...
Hi guys, I'm having a bit of trouble splitting the RHS of the following expression into real and imaginary parts:
(χ'+iχ")/A = \frac{1}{ω-ω_{0}-iγ/2}
(It's to find expressions for absorption coefficient and index of refraction, but that's irrelevant).
I've defined a = ω-ω_{0} and b =...