Hi everyone, I've recently been bugged by a question I can't seem to find a reasonable answer to. It's about an apparent contradiction between how the wave equation is supposed to evolve in time according to the schrodinger equation and the measurement formalism in QM.(adsbygoogle = window.adsbygoogle || []).push({});

Suppose I have any physical system, for the sake of concreteness let's say it's a single slit setup with photons being fired at a single slit one at a time and hitting a screen that records where they hit. The usual way I hear this described is that the photons each have some wavefunction that describes the probability distribution of being at a particular position, and the screen measures the position from the probability distribution of the wavefunction. The same exact experiment will lead to different results for different photons because its wavefunction only gives probabilities.

On the other hand, the wave function is supposed to evolve in time according to the Schrodinger equation. Given an initial condition and valid boundary conditions, there is a unique solution for the wavefunction as a function of time. Here is the apparent contradiction. At the end of the slit experiment the wavefunction is different in different trials with the same exact initial conditions and boundary conditions. I understand that the screen interacts with the photon, but in principle, we could include the screen in the system we describe and put into the S. Eq. If there is a human watching, we could include the atoms in his body as well. I see no way around the fact that, on the one hand, the S.Eq gives a unique solution for the wavefunction at the end, while the experiments give many possibilities.

Does anyone see a resolution to this? I'm sure there must be a simple explanation, but I just can't find it no matter how hard I try.

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# How does the Schrödinger equation lead to the QM theory of measurement?

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