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Could someone help clarify what the diff. is between j0 and n0 as discussed in todays lecture on pg 143 ?

I know it was a ? in class, but iam not clear on what the answer was.

j0 are the Bessel functions and n0 are the Neumann functions. We only deal with Bessel functions in physics, because the Neumann functions blow up at the origin and therefore have no physical significance. It's just like with the Legendre polynomials that we discussed in class–Legendre functions are second order equations, meaning that there are two solutions. The first kind are the ones we use P(z), but there is a second kind Q(z) that we do not discuss because they diverge at z=1.

Why is it so important to find simultaneous eigenstates, when we have compatible operators. Griffths does with the angular momentum quantities, but I don't see why it is so important. What does it mean to be simultaneous? Does it just mean that you can measure both quantities at the same time or are they other implications that go along with this?

Thanks!

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