Thanks for your answer. I can derive the second equantion using your transformation.
But in both expressions, a and a^{\dagger} are annihilation and creation operators, respectively, and they are real. Is the transformation still valid?
Hi, I have a question about two different expressions of Jaynes-Cummings Hamiltonian
H=\Delta_c a^{\dagger}a+\Delta_a \sigma_{+} \sigma_{-} +
g (a^{\dagger}\sigma_{-} +a\sigma_{+} )
and
H=\Delta_c a^{\dagger}a+\Delta_a \sigma_{+} \sigma_{-} +i
g (a^{\dagger}\sigma_{-} -a\sigma_{+}...