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No. A single measurement can't tell you if the state was in a superposition or it was a pure state. In order to be able to do that you must have knowledge of how the state was prepared, which means you must have gauged your apparatus and therefore performed a statistically relevant number of measurements on the very same state many times and taken note of ...


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$\newcommand{\ket}[1]{\lvert #1 \rangle}$There is no such thing as "looking like a collapsed wavefunction", even if you believe there's collapse. Let's go to the finite dimensional case and have a simple two-level spin system, that is, our Hilbert space is spanned by, e.g., the definite spin states in the $z$-direction ...


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If a given state is an eigenstate of a particular observable then that observable has a standard deviation of 0, however that says nothing about the distribution of any other observables. The extreme example of this are the eigenstates of position and momentum; a momentum eigenstate is represented by delta function in momentum space but in space it is ...


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First of all, I'm not a physics specialist. In my opinion, the reason why I'm typing this text at this second and the next one is that we are working inside another parameter. In other words, we are dealing with a "computer" object that is made up of other quantum objects, but that molecules are working as a computer. Once we catch computer, it is always ...


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Your linked article ('How do probabilities emergeā€¦') only seems to explain why each universe is internally consistent and acts according to what we would statistically expect. The argument pretty much goes that it is of course entirely possible to get weird behavior, but it is precisely as likely to occur as in a single universe obeying the known physical ...


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When you measure an observable over a certain state, any possible outcome lies within the physical spectrum of the observable itself (which can be shown to coincide with the algebraic notion of spectrum for linear operators). So after the measurement has given you a value, say, $\lambda$, any other measurement on the system will give you $\lambda$ again with ...


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This phenomenon is called the collapse of the wave function. It is one of the tenets of the Copenhagen interpretation of quantum mechanics. The eigenstates $|\xi_i\rangle$ of the $\Xi$ operator form a complete set. From linear algebra we have $$I=\sum_i|\xi_i\rangle\langle \xi_i|$$ where $I$ is the identity operator. We apply this to the state vector ...


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I post this answer to check my understanding. Imagine a wavefunction in 1 dimensions with a known energy and momentum it's wavefunction will be: $$\Psi(x, t) = e^{i(kx-\omega t)} = e^{i(px-E t)/\hbar}$$ With some calculus and algebra you can derive the momentum operator and get this: $$-i\hbar \partial_x \Psi = p \Psi$$ There $-i\hbar \partial_x$ is ...



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