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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?

Griffiths is finding <math>\Chi_{+}^x</math> and <math>\Chi_{-}^x</math> in terms of <math>\Chi_{+}^z</math> and <math>\Chi_{-}^z</math>. This is somewhat arbitrary because x and y are defined arbitrarily, but the way Griffiths does it is presumably what people have found to be easiest to work with.

As for why it's done, suppose that you instead change coordinate systems so x and z are switched. Now, you can express the new z (the old x) simply, but you don't know how to express the new x (the old z). To understand the system, you need to be able to express the eigenstates of spin in one direction in terms of those in another direction.

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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