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So in reviewing for the test, I was going back through the textbook and realized I was still confused on something. On page 175, they ask, 'what if you chose to measure Sx?' From there, they go forward with determining eigenvalues of the Sx matrix, and then they proceed to multiply those by some arbitrary vector, alpha beta. Why this arbitrary vector? We know we're working with Chi+ and Chi-, why do we need to redefine them? What exactly is Chi+(x)? I'm just not understanding why we can't just use the basic Chi+ with the (1 0) and (0 1) vectors?

In the text Griffiths says that the corrections we apply in perturbation theory yield surprisingly accurate results for the Energy of the perturbed system but fairly terrible wavefunctions. Can anyone explain why the wavefunctions aren't approximated well? -and furthermore, how the energy is well-approximated while simultaneously the wavefunctions aren't?

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