Is there a guide to using the density matrix formalism in quantum mechanics?

peterjaybee
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Hello, I am looking for a guide to quantum mechanics and the density matrix formalism which uses the Einstein summation convention. Does such a guide exist?
 
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I ask because bra's and ket's seem to behave in a similar manner to co-varient and contra-varient vectors. I guess this is not a coincidence.
 
peterjaybee said:
I ask because bra's and ket's seem to behave in a similar manner to co-varient and contra-varient vectors. I guess this is not a coincidence.

No. See the section ''What are bras and kets'' in Chapter A1 of my theoretical physics FAQ at
http://arnold-neumaier.at/physfaq/physics-faq.html#A1
 
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Thread 'Lesser Green's function'
The lesser Green's function is defined as: $$G^{<}(t,t')=i\langle C_{\nu}^{\dagger}(t')C_{\nu}(t)\rangle=i\bra{n}C_{\nu}^{\dagger}(t')C_{\nu}(t)\ket{n}$$ where ##\ket{n}## is the many particle ground state. $$G^{<}(t,t')=i\bra{n}e^{iHt'}C_{\nu}^{\dagger}(0)e^{-iHt'}e^{iHt}C_{\nu}(0)e^{-iHt}\ket{n}$$ First consider the case t <t' Define, $$\ket{\alpha}=e^{-iH(t'-t)}C_{\nu}(0)e^{-iHt}\ket{n}$$ $$\ket{\beta}=C_{\nu}(0)e^{-iHt'}\ket{n}$$ $$G^{<}(t,t')=i\bra{\beta}\ket{\alpha}$$ ##\ket{\alpha}##...

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