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## Main Question or Discussion Point

Hi, I have a question about two different expressions of Jaynes-Cummings Hamiltonian

[itex]H=\Delta_c a^{\dagger}a+\Delta_a \sigma_{+} \sigma_{-} +

g (a^{\dagger}\sigma_{-} +a\sigma_{+} )[/itex]

and

[itex]H=\Delta_c a^{\dagger}a+\Delta_a \sigma_{+} \sigma_{-} +i

g (a^{\dagger}\sigma_{-} -a\sigma_{+} )[/itex].[itex](\hbar=1)[/itex]

I read them from different papers and books.

Why are they equal, and how to derive one from another?

How to choose the appropriate expression when utilizing the Jaynes-Cummings Hamiltonian?

Thanks!

[itex]H=\Delta_c a^{\dagger}a+\Delta_a \sigma_{+} \sigma_{-} +

g (a^{\dagger}\sigma_{-} +a\sigma_{+} )[/itex]

and

[itex]H=\Delta_c a^{\dagger}a+\Delta_a \sigma_{+} \sigma_{-} +i

g (a^{\dagger}\sigma_{-} -a\sigma_{+} )[/itex].[itex](\hbar=1)[/itex]

I read them from different papers and books.

Why are they equal, and how to derive one from another?

How to choose the appropriate expression when utilizing the Jaynes-Cummings Hamiltonian?

Thanks!

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