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I'm still a little confused as to how we can show that <f_p'|f_p> = d(p-p') and what the so called Dirac orthonormality is really saying.

In problem 3.13 we had to show three parts. I'm a little confused as to how they are related. Particularly, is part a (the commutator identity) somehow relevant to part c?

Now that I'm getting a better understanding of the new notation, can someone explain to me if it's possible to have multiple eigenvalues for the same state? I vaguely remember hearing something like this before I fully understood its implications. How does this work statistically?

My understanding is that the space-momentum uncertainty principle is analogous to the time-energy one. What are the implications of this? Should I change my understanding of how momentum and energy are related? Particularly, I'm having trouble understanding how the concept of mass fits in… Maybe I'm just way overthinking it, or maybe my grasp on relativity is just not strong enough.

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