- #1
barnflakes
- 156
- 4
Can someone explain the attached image for me please?
I do not understand how [tex]2\delta_{k, k'}a_{k'}^{\dagger}a_{k}[/tex] becomes [tex]
a_{k}^{\dagger}a_{k} + a_{-k}^{\dagger}a_{-k} [/tex] to me it should just be [tex]2a_{k}^{\dagger}a_{k}[/tex]
and also I do not understand how [tex]e^{-ik}a_{-k}a_{k} + e^{ik}a_{-k}^{\dagger}a_{k}^{\dagger} = \cos(k) a_{-k}a_{k} + \cos(k) a_{-k}^{\dagger}a_{k}^{\dagger}[/tex]
I do not understand how [tex]2\delta_{k, k'}a_{k'}^{\dagger}a_{k}[/tex] becomes [tex]
a_{k}^{\dagger}a_{k} + a_{-k}^{\dagger}a_{-k} [/tex] to me it should just be [tex]2a_{k}^{\dagger}a_{k}[/tex]
and also I do not understand how [tex]e^{-ik}a_{-k}a_{k} + e^{ik}a_{-k}^{\dagger}a_{k}^{\dagger} = \cos(k) a_{-k}a_{k} + \cos(k) a_{-k}^{\dagger}a_{k}^{\dagger}[/tex]
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