I am taking an intro. to quantum mechanics course and was taught that superposition exists until we measure the system which makes the wave function of a quantum system collapse. I have a basic understanding of superposition, probabilities etc. However, what I couldn't manage to understand is how we are sure if our measurement does affect the system if we don't know what would happen to the system if we don't measure it.

A more detailed explanation

I am currently trying to understand quantized energy levels, not just recognize the formula and patterns. So, I have 2 complex numbers that define the probability of an electron to be in either ground or 1st excited state. If we don't measure the system the electron is in superposition. When we measure the electron, its wave function collapses to either ground or 1st excited state, but again how we can be certain on that it hadn't been in the system that we measured? I couldn't find directly answers related to this questions, but rather on the existence of superposition, which in my case I accept. I must be missing a logical explanation, but I can't find.


1 Answer 1


The way that we know how a system is affected after a measurement - namely that traditionally, one says that it transitions into an eigenstate of the measured observable* - is by having measured things twice.

The way this was explained to me in my undergrad was that when measuring the spin of the same particle twice, it was always found to have the same value. So the only state we can logically assign to it after the first measurement is an eigenstate of spin with the same value.

As for your question of "how do we know it wasn't already in an eigenstate" - that is because of the following. Suppose one prepares the system in the same initial state, lets it evolve in a known way and then measures it. Doing this process multiple times, one doesn't just get the same result over and over. Instead, with no apparent explanation, each run gives a different outcome. That is why we can't just assign one single eigenstate to the system before measurement. Multiple outcomes are possible despite (to our best knowledge) the initial conditions being the same.

*actually this postulate is only kinda right-ish, and doesn't work for all types of measurements. In particular it gives inaccurate results for continuous variables like $x$ and $p$.

  • $\begingroup$ each run gives a different outcome. I couldn't think that this may be the reason, thank you! $\endgroup$ Apr 8, 2023 at 11:38
  • $\begingroup$ glad to help! -- $\endgroup$ Apr 8, 2023 at 16:51

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