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Before going further, I would suggest you to read Chapter 13 ("Spinors") of R.Wald's book "General Relativity". In that chapter, you will see that 2-spinors are simply vectors living in a two-dimensional complex vector space. The capital letters in the indices are simply the abstract index notation for these vectors (see Section 2.4 in Chapter 2 of the same ...


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First I want to point out that most of these questions do not bring up issues specific to Bohmian mechanics. That's not a criticism, I'm just pointing out that these notations and concepts are already employed in standard quantum mechanics, or even in classical mechanics. I am going to answer this a little casually, and then make my answer "community ...


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$\newcommand{\ket}[1]{\lvert #1 \rangle} \newcommand{\bra}[1]{\langle #1 \rvert}$The states of a quantum system are nothing else than the abstract vectors in the Hilbert space of states $\mathcal{H}$. For one particle, given a basis of position eigenkets $\ket{x}$ with $\hat{x}\ket{x_0} = x_0\ket{x_0}$ and a state $\ket{i}\in\mathcal{H}$, the wavefunction is ...


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If we know there is a particle(s) in state $i_1$ why do we need $r_1$? Does the state $i_1$ not specify position? The fact that the particle is in a state $|\psi\rangle$ does not specify the particle's position - it specifies the wave-function $$ \langle x | \psi \rangle = \psi(x) $$ from which one can find $$|\psi(x)|^2$$ This is the probability ...



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