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I am in my Undergraduate Quantum Mechanics class right now and it has been great fun so far. However, I am still hooked up on a topic that just does not click with me, but is of vital importance. I need help in understanding what the wavefunction does and why it does it when we measure the:

a)Position

b)Momentum

c)Energy

I get that when we measure the position, the probability density "collapses" into a delta function at the measured value. The many momenta needed to create that spike, quickly make the probability density spread out again, so if we measure the position immediatly after, we will not necessarily get the same value again.

We recently had a test where the system was a particle in an infinite square well. He asked us that if we measure the particle's location and find it is at some value, will subsequent measurements yield the same result.

His response was that this is an eigenfunction of position, not of energy. Since the position operator does not commute with the energy operator for a square well, this wavefunction is not a stationary state and will evolve in time.

And then we go on to measuring the energy. He asked if we measure the energy, will subsequent measurements yield the same value? He said that it is not an eigenstate of energy. Therefore it won't evolve in time and repeated measurements of energy will give the same result.

I am very confused at the moment, and I would greatly appreciate any help you could give me. Thank you for your time.

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# I need help in understanding the measurement process.

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