A quantum system under constant observation

[nashed]

To start off I'd like to apologize ahead of time for the grammatical errors and lack of eloquence that are sure to follow, it's the middle of the night and my mind is wandering but my cognitive capacity to express my self is pretty low at this time.

With that out of the way, I'd like to ask about something which has been bothering me for quite a time now, I finished my introductory QM course about a month ago and one of the postulates that was mentioned was that upon measurement the state of the system will change/collapse/whatever you'd like to call it to the state corresponding to the measurement, now let's look for example at a harmonic oscillator which is something I've observed in labs ( the classical experiment any how), the thing is that for the whole length of the experiment I had my eyes on the oscillator and classically that's fine, but with QM it seems like it should be collapsing all the time while trying to evolve in time in accordance with the solution for Schrödinger's equation, so can anyone shed light on how am I supposed to understand this situation?

To add to the above, I'm aware of the correspondence principle and have seen that for large energies the probability distribution starts to look like the classical distribution, but again this solution fails to take into consideration that the system is under constant observation.

 

[stevendaryl]

This is sort of the topic of the "quantum zeno effect"--to have a system under constant observation.

http://www.news.cornell.edu/stories/2015/10/zeno-effect-verified-atoms-wont-move-while-you-watch

 

[hilbert2]

Let's say you have a quantum harmonic oscillator with one degree of freedom called $x$. Then you measure $x$ at some high accuracy (with maximum error some small quantity $\Delta x$) and do that repeatedly with a very short time interval $\Delta t$ between the measurements. What happens when you decrease both $\Delta x$ and $\Delta t$ such that they approach zero? The more accurate the measurement of $x$ becomes the less accurate your knowledge of the momentum $p_x$ becomes, and the longer distance the particle can move in the time interval $\Delta t$. Therefore you can't get a situation where you have real time knowledge of the value of $x$. This is how I understand it, anyway.

 

[Strilanc]

for the whole length of the experiment I had my eyes on the oscillator and classically that's fine, but with QM it seems like it should be collapsing all the time while trying to evolve in time in accordance with the solution for Schrödinger's equation, so can anyone shed light on how am I supposed to understand this situation?

You've confused the lay meaning of "observe" with the technical meaning in quantum mechanics. Pointing your face towards a quantum system doesn't affect whether or not it's being measured. What matters is if the system interacted with the surrounding environment in a thermodynamically irreversible way or not.

To understand the situation you just do the math. How strong is the interaction with the outside? How long until we stop protecting the system? What's the Hamiltonian?

Keeping all of that in mind... if you do set up a situation where a quantum system is being measured again and again at a high rate, you'll find that it tends to stay in the same state. Even against forces that would normally cause it to evolve. See: Quantum Zeno Effect. It's basically the same thing as putting a diagonal polarizer between two orthogonal polarizers to allow some of the light through, but taken to the limit.

 

[vanhees71]

I'd say it's simply the coupling of the system with the measurement device. There's nothing myterious about it, although with fascinating "very quantum" properties, like keeping a system in an unstable state for very long (i.e., much longer than the lifetime of the state) by "observing" it. As mentioned in previous postings, this is then known the "quantum Zeno effect" to make it even more exciting :-).