In the theory of degenerate perturbation in Sakurai’s textbook, Modern Quantum Mechanics Chapter 5, the perturbed Hamiltonian is [itex] H|l\rangle=(H_0 +\lambda V) |l\rangle =E|l\rangle [/itex] which is written as [itex]0=(E-H_0-\lambda V) |l\rangle [/itex](the formula (5.2.2)). By projecting [itex]P_1[/itex] from the left ([itex]P_1=1-P_0[/itex] and [itex]P_0[/itex] is projection operator onto the degenerate subspace):(adsbygoogle = window.adsbygoogle || []).push({});

[itex]-\lambda P_1 V P_0|l\rangle +(E-H_0-\lambda P_1 V)P_1|l\rangle=0 [/itex] (5.2.4)

Then from this, the formula below is obtained:

[itex]P_1|l\rangle =P_1 \frac{\lambda}{E-H_0-\lambda P_1 V P_1}P_1 V P_0|l\rangle [/itex] (5.2.5)

But I never can reach to (5.2.5) from (5.2.4). Could anyone please help me?

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# Degenerate perturbation theory (Sakurai's textbook)

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