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I’m new in QM. I have a simple question: when one says that the wavefunction collapses, is it the same as saying that the variance of an observable is 0? Thanks.
Thanks, that was very helpful!Isaac0427 said:Pretty much, but with a caveat. Technically, it's not just saying that the variance is zero, but the state of the particle has changed to the state where the variance is zero (there's still a caveat). Although I think this does tread a little bit into interpretations, as some interpretations disagree with the whole concept of collapse.
In the case of spin or angular momentum, your statement about the variance is correct. If you measure, say, the z-component of the spin of an electron to be up, then the electron, no matter what state it was in before, changes to be in the state of being spin up in the z-component (100% probability). This would also work if you measure the energy of a particle in a bound state (which could be in a superposition of multiple energy states).
Here's the caveat: a particle can never have a precisely defined position. The variance can never be zero, and therefore one can never precisely measure the position of a particle. The wavefunction would collapse to a spike around the point it is measured at, but it wouldn't be exactly a Dirac delta, which is the only "wavefunction" with a precisely defined position. Additionally, this collapsed state would be short-lived, due to Schrodinger evolution.
To see this in action, look at this simulation. To see it best, switch to a constant potential, pause time, and click "make quantum measurement" (and notice how the spike still isn't a perfect delta function). Then progress time to see what happens.
A wavefunction collapse is a phenomenon in quantum mechanics where the superposition of multiple possible states of a system collapses into a single definite state upon measurement or observation. This means that the system can only exist in one state, rather than multiple states at once.
The exact cause of a wavefunction collapse is still debated in the scientific community. Some theories suggest that it is due to the interaction between the system being measured and the measuring apparatus. Others propose that it is a result of the conscious observation of the system.
No, a wavefunction collapse cannot be reversed. Once a system has collapsed into a definite state, it cannot return to a state of superposition. This is one of the key principles of quantum mechanics.
The collapse of a wavefunction is significant because it is a fundamental aspect of quantum mechanics. It helps explain the behavior of particles at the subatomic level and has important implications for fields such as quantum computing and quantum cryptography.
No, the collapse of a wavefunction is not a deterministic process. It is a probabilistic phenomenon, meaning that the outcome of a measurement or observation cannot be predicted with certainty. This is another key principle of quantum mechanics.