- #1

climbon

- 18

- 0

I am reading a paper and can't get the same answer they do, they have;

[tex]

H= -i\hbar \sum_{\lambda} \int dK (a_{(k,\lambda)} g_{(1;K,\lambda)} \sigma_{1}^{+} e^{-i(\omega_{k}- \omega)t} - H.C )

[/tex]

Then states they do a formal integration of the Heissenberg equation for [tex] a_{k,\lambda}(t) [/tex] using the above Hamiltonian, they get;

[tex]

a_{k,\lambda}(t) = a_{k,\lambda}(t_{0}) + \int_{t_{0}}^{t} dt^{'} g^{*} \sigma_{1}^{-}(t^{'}) e^{-i(\omega_{k}- \omega)t^{'}}

[/tex]

Could anyone help me as to how they get this answer from the Heissenberg equation...you be greatly appreciated!

Thanks.