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Does observation collapse the wave function, thus preventing an object from tunneling to a classically forbidden region?

If I understand correctly, observation causes objects to collapse into the state in which they were observed, so there will no longer be a probability of finding them elsewhere. Then if I am somehow measuring the position of an object, does that mean it can't tunnel as long as I continue to observe it? For example, can my hand tunnel to the moon, even though I am looking at it right now, thus measuring its position? How does measurement affect the possibility of tunneling?

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  • $\begingroup$ have a look at this question physics.stackexchange.com/questions/92263/… $\endgroup$
    – anna v
    Jan 6 '14 at 9:19
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    $\begingroup$ The search phrase you want is "Quantum Zeno Effect" or "Quantum watched pot". Some papers (by DOI and or traditional refernce) 10.1103/PhysRevA.41.2295; Phys. Rev. Lett. 87, 040402 (2001); Physical Phys. Rev. Lett. 97, 260402 (2006); Reviews: Reviews of Modern Physics, Vol. 75, January 2003. The short version is that observation can effect macroscopic evolution. Still trying to convince a student to do a paper on this. $\endgroup$ Jan 6 '14 at 16:44
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Prior to measurement you can have a wavefunction that has some contribution beyond a potential barrier. Thus if you were to measure the position of the particle you have some probability to find that the particle would have tunnelled to the other side of the barrier. Observing the particles position doesn't stop the particle from tunnelling, it checks where the particle is.

That being said after measuring the position of a particle it becomes a position eigenstate and the wavefunction becomes a delta function at whatever position you measured. If left unobserved then the wave function will evolve in time and spread out again.

If the position of the wavefunction is measured often enough it will not have a chance to evolve in time and spread out, thus stopping it from tunnelling. That being said, the time it takes a wavefunction to spread out may be really short making it difficult to measure the wavefunction quickly enough to stop it from spreading out prior to the next measurement

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  • $\begingroup$ Is there such a thing as "continuous" measurement then? That is, can I observe a particle only at specific points in time, or can I track a particle over some interval of time, measuring its position? I guess the uncertainty principle forbids the latter? $\endgroup$
    – Andrea
    Jan 6 '14 at 10:19
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    $\begingroup$ I think you've answered you're own question. In Quantum Mechanics we never speak of continuous measurements because it isn't possible to set that up. One way to think about that is the uncertainty principle. Alternatively, thinking microscopically, a measurement consists of an interaction an exchange of a photon between particles. This can't happen continuously. $\endgroup$
    – JeffDror
    Jan 6 '14 at 14:21

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