New answers tagged observables
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There is a difference between the mathematical treatment of Quantum Mechanics, and the pratical job of an experimenter.
Quantum mechanics says that the outcome of a measure is a particular eigenvalue of an operator:
$$ Particle \, Position : X^i(t)|\psi> = x^i(t)|\psi>$$
$$ Particle \, Spin : S_z\psi> = s_z|\psi>$$
$$ Fields : ...
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If you are able to produce multiple copies of the same pure quantum state, then it is possible to reconstruct the wavefunction. In that case, you need a relatively precise experiment, as just measuring the position and building a histogram will only give you the mod-squared of the wavefunction. To get some information of the phase, you might try measuring ...
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You can measure the amplitude squared of the wave function if you have many copies of the system. You can then make a histogram of the recorded observations of the systems. This histogram will tend to the amplitude squared of the wave function as the number of copies tends to infinity.
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It might be true for those systems whose only degrees of freedom are time and position. However, there are other internal components such as spin that do not directly reduce to position or time. So this is one example where this statement fails.
Having said that, I would not discount it entirely. Spin can certainly be measured by observing trajectories of ...
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One point to consider, although not a definitive answer, is the following. The validity of the pilot-wave theory (Bohmian mechanics) relies on the truth of Feynman & Hibbs' postulate (F&H). This is because the pilot-wave theory only makes predictions about the positions of all particles, which along with the unobservable wave function constitute a ...
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