What happens after a quantum measurement?

In this video we study the time evolution of a quantum particle after its position is measured.

📚Time evolution in quantum mechanics is governed by the Schrödinger equation, and here we use it to study the time evolution of a quantum particle in an infinite square well potential. We first look at a superposition state made of two energy eigenstates, which shows periodic oscillations of the probability density of the particle. We then look at how a quantum particle evolves in time after it is found to be at a certain position. We find that the wave function rapidly spreads so that at a later time the particle could be anywhere inside the box with similar probability.

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👩‍💻 GITHUB

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Director and writer: BM
Producer and designer: MC

[jhanzaibhumayun]

Just started our QM course. This is a godsend!

[pier_]

Thank you for the great video and the explanation. Real cases really help to put together all the principles we study. Well done!👍

[georgerevell]

How is this powerful video not more popular? People scared a little undergrad maths!?

[SergeyPopach]

So, applying the measurement operation triggers collapse of wave funciton and initiates a time evolution of the quantum state and after measurement it comes back to its original (stationary) state (when solving a eigenvalue for Hamiltonian)?

[wadelamble]

Thanks for the videos. Incredible content! In the Schroedinger equation video, I thought you said that we solve in the energy basis and gave a general recipe for solving physical scenarios using the eigenvalue equation in the energy basis, but in this video and the infinite square well, you seem to use the position basis. Am I mistaken in equating these approaches? Are there examples of problems solved in the energy basis. Would Psi then not be a function of position? If so, how would I convert back to the position basis.

[alexanderheller]

13:38 must be the coolest thing I've seen in quantum mechanics. It makes me think of that quote... "How do we know the moon is there when we're not looking at it?"

[mjjnvyd]

Then, how do we prepare a quantum state before the measurement?

[gnyszbr]

This will be a more practical question, but how do we know the amount of states our superposition can collapse into in a real example? I mean sure the energy we put in while constructing the system must at least be higher than the nth energy eigenstate's energy amount in order to have n states but then what happens when we put in a "nth state" amount of energy and superposition collapses into (n-1)th state? Isn't the energy lost here? Or is it because our way of putting energy in the first place also includes some uncertainty so there is a range including both higher results and lower results?

[vancuongpham]

Thanks for your video, I am a starter, may I ask you some questions about this one,
1. if particle is at x0 and and the function of particle is Delta (x-x0), so what I understand here that the variance of x = 0, at least at the mathematical theory. It means if I take a measurement at that time, we can collect the absolute value without any error? Can you correct me?
2. and the second inquiry is about that you take a set of the eigen function of energy as a set of the eigen function of position, I confuse this a lot, because as far I know, they have their own eigen function (I understand eigen function and associated wave function are the same?) for every eigen value, maybe this a silly question,
3. The 3rd question is if x0 is eigen value, so what is eigen function (out of the above set of eigen function) for this eigen value.
4. And the 4th question, I saw in your video the E (j=1, k=2), but actually, I remember, it just take only 1 function after the measurement, is it right?
I hope your clearing to help me more,
Thanks again for your clip,

[khoanguyen]

If i take a stationary state and the wave function collpased at x_o, does it also evolves to wave function with constant probability as the end of the video? Or it evolves back to the same stationary state?

[geraldpellegrini]

Summation of Heisenberg's time dependent matrix elements solves this "mind blowing" problem. See emails to you on July 31 9:30 am and August 14 8:45 am. Why no reply??

[geraldpellegrini]

If the particle in a box is isolated it is forced to be in an energy eigenstate. Contrary to Ehrenfest's theorem the classical correspondence is NOT achieved for this isolated system!
According to the Ehrenfest equation of motion the expectation value of particle positions is stationary for this eigenstate, which is not the classical correspondence motion!!

[geraldpellegrini]

Summation of Heisenberg's time dependant matrix elements seems to solve this "mind blowing" problem. See my emails to you on July 31 9:30am, and August 14 8:45am.

[geraldpellegrini]

This video should demonstrate this "mind blowing" approach to the particle's motion is completely unrealistic and wrong! Especially in light of the fact that summation of Heisenberg's time dependant matrix elements for a given energy eigenstate gives the classical motion in the classical limit.

[geraldpellegrini]

Why does no one see this a proof the standard use of a single state 'wave function' as a complete description of the particle motion is WRONG!

[geraldpellegrini]

What happens after you measure the energy?? All probability distributions are time independent and all motion stops, correct? That's even more "mind blowing"

[geraldpellegrini]

Why do you believe this rediculous conclusion? There comes a time when you have to make sense!!

[geraldpellegrini]

Does everyone actually believe this rediculous conclusion?

[schmetterling]

There is no such thing as an "after a measurement". A measurement is irreversible, i.e. it stays around forever.