Problem understanding Green's function equality in Messiah QM II

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SUMMARY

The discussion centers on the Green's function equality presented in Messiah's "Quantum Mechanics II," specifically in Chapter 16.3.2. The user Tobe questions the transition between equations (16.60) and (16.61), particularly the presence of a '1' in the numerator of the first term. The response clarifies that the expression simplifies to \(\frac{1}{z-H_0}\) due to the cancellation of terms, confirming the equality. This exchange highlights the importance of understanding operator manipulation in quantum mechanics.

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tobe
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Hi,

It's about green's function in the book Messiah - Quantum Mechanics II - Chapter 16.3.2
(see http://books.google.de/books?id=OJ1...dq=messiah+quantenmechanik+kapitel+16.3&hl=de). The book actually is in german, but I guess that doesn't matter understanding the formulas.
I don't understand the last equality between eq. (16.60) & (16.61). Why is there in the first term's nominator a 1 (instead of "z - H_o - lV")? Can somebody help me out?


Cheers
Tobe
 
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Because the first term is

[tex] \frac{1}{z-H_0} \left( z - H_0 -\lambda V \right) \frac{1}{z - H_0 -\lambda V} = \frac{1}{z-H_0}.[/tex]
 
oh dammit! :D

thanks man!
 

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