I'm looking at the beginning of of Chapter 6 of the 2nd edition of Griffiths(adsbygoogle = window.adsbygoogle || []).push({}); Introduction to Quantum Mechanics.

He starts out by writing the hamiltonian for a system we'd like to solve as the sum of a hamiltonian with a known solution and a small perturbation:

[tex] H^0 + \lambda H^\prime [/tex]

He says that lambda is meant to be a small number for now, but later it will be set to 1, and when it is, that will be the true Hamiltonian. My first question is huh? Why? Then later he says that the eigenfunctions and eigenvalues can be written as a power series in lambda. E.g.:

[tex] \psi_n = \psi_n^0 + \lambda \psi_n^1 + \lambda^2 \psi_n^2 + \cdots [/tex]

Again, huh? How can can just write this down? How does he know that [itex] \psi_n [/itex] can be written in this form? Why does the lambda from the perturbation appear in the corrections to the wavefunction and allowed energies in this way? It just seems to come from nowhere. Am I missing something?

Also, what is meant by "first order correction" and "second order correction?" First order in what? The above equation would seem to indicate that the answer is "in lambda." But later on, he claims that lambda is just a "device for keeping track of the orders" and sets it to 1, effectively eliminating it from the equation. So what is it intrinsically about [itex] \psi_n^1 [/itex] that makes it "first order" for example?

I'm sorry for being such a dunce, but I am having a hard time understanding where he's coming from.

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# Perturbation Theory

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