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I will stick my neck out without researching this. I think this is a matter of the Pauli exclusion principle.

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The state -1 which you mention is an eigenstate of the operator A, and not of the hamiltonian. You showed that the hamiltonian and A don't commute since the hamiltonian wasn't diagonal in the basis of A's eigen states + and -. Ignoring the bra-ket notation for now, |-> = $\frac {1}{\sqrt{2}} (E1 + E2)$ Now since E1 and E2 are orthonormal too (check by ...

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There are explanations for why the probability of a measurement of a particular observable is the square amplitude of the relevant eigenstates. The square amplitude is the only quantity that fits the calculus or of probability, and the rules of decision theory, and quantum physics: http://arxiv.org/abs/quant-ph/9906015 http://arxiv.org/abs/0906.2718. The ...

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I know that the usual interpretation of the wavefunction in QM is that it´s a probability distribution of measurable quantities. It is a postulate that is necessary to choose the subset of mathematical sets that can be useful to modeling nature. The postulate was chosen because observations were fitted by the hypothesis. Not a deterministic ...

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The spin state is given as a linear combination of spin up and spin down states. So $$\psi=c_+| z +\rangle+c_-| z -\rangle$$ The square of the modulus of the complex coefficients $c_+$ and $c_-$ represent the probabilities of each associated base kets. When you multiply $\psi$ by a constant, the state will not change as a ket and a constant times that ...

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The measurements are repeated $N$ times for the same physical conditions; there are thus $N$ points for this single datum, which will be reported as the mean of the sample , along with the measured standard deviation. The interval is conventional, based on common usage. This makes it easier to interpret the meaning of the reported measurements. ...

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Robert Griffiths is quite fond of Mach-Zehnder experiments as useful windows into interpreting quantum foundations, and he presents calculations for some toy models of M-Z interferometers in Chapter 13 of his book, Consistent Quantum Theory. As a caution, most of this book is written to parallel the consistent quantum histories formulation of quantum ...

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