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Traditional collapse is from wave-function to wave-function. The result of the measurement is something different (but related). The result of the measurement
by kgwgk 8y ago
Traditional collapse is from wave-function to wave-function. The result of the measurement is something different (but related).
The result of the measurement is one of the eigen-values of the observable operator (that's the essence of quantum mechanics, the set of outcomes is "quantized").
If the eigen-value observed is non-degenerate there is only one wave-function that corresponds to that pure state (i.e. the corresponding eigen-function). Immediately after the measurement, that will be the wave-function describing the system (and then will evolve according to Schroedinger's equation). In the general degenerate case, it will be the projection of the wavefunction before the measurement on the corresponding subspace.
Depending on what you measure the probability density corresponding to the after-measurement wave-function may or may not be concentrated at some point. It will happen if you measure the position (you know where it is know!). But if you measure the momentum, the location becomes completely undetermined.
- scotty79 8y agoThat's great. So, pretty much I have correct intuitive understanding of quantum mechanics (except with that degenerate thing which I never encounterd before). Thank you for your comments. At least now I can be now at peace when I read pop-sci articles about quantum knowing that they are just using extreme simplification (to the point of being wrong) but the actual current understanding is same as I believe and I'm in no obligation to share my insights. ;-)
- kgwgk 8y agoRemember: "I think I can safely say that nobody understands quantum mechanics." ~ Richard Feynman Edit: Degenerate means that the measurement doesn't completely determine the state of the system. In that case the state before the measurement is projected onto the subspace of states compatible with the measurement, I think this may be more or less what you meant by "narrowing down the possibilities".