Some problems about Quantum tunnelling

[ShayanJ]

In quantum tunnelling,as I understood,when a particle reaches the boundry of a potential barrier,it is possible,that the particle passes the barrier and it is performed like disappearing before the barrier and appearing after it.If the latter is the case,so there should be a motin which is faster than light.But it can't be correct.
Another problem is that the probability for the presence of particle in the middle of the barrier,is not zero.I think it means that the particle just moves inside the barrier and then outside of it.But it can't be correct too because the particle can't do that because of the high pottential difference.
Its so much confusing.Could you help?
thanks

 

[SpectraCat]

In quantum tunnelling,as I understood,when a particle reaches the boundry of a potential barrier,it is possible,that the particle passes the barrier and it is performed like disappearing before the barrier and appearing after it.If the latter is the case,so there should be a motin which is faster than light.But it can't be correct.
Another problem is that the probability for the presence of particle in the middle of the barrier,is not zero.I think it means that the particle just moves inside the barrier and then outside of it.But it can't be correct too because the particle can't do that because of the high pottential difference.
Its so much confusing.Could you help?
thanks

One problem is that you are thinking of particles classically, while analyzing a quantum mechanical phenomenon. In standard QM, particles don't have the sorts of well-defined trajectories that you are imagining, so these sorts of inquiries have to be phrased in a different way to make physical sense.

In standard QM, particles are spatially delocalized, so that even in the free particle case you seem to be thinking about, they are properly represented as a wavepacket. When a wavepacket interacts with a barrier, part of it is reflected, and part of it is transmitted via tunneling. So, if you now do a measurement on the quantum system, there is a finite probability that you will detect that the particle has tunneled through to the other side. http://labspace.open.ac.uk/mod/resource/view.php?id=347298" may help you understand the phenomenon of wavepacket tunneling better.

Remember that in QM, you can only make probabilistic statements about physical properties before you have measured them. Now, if you want to say something like, "Fine. So I will measure the particle just before it hits the barrier, and then I will measure just on the other side immediately after, to see if it has tunneled." You can of course do that, but if you want to measure the wavepacket in a narrow region of space, then you will find the that the process of measuring it necessarily entails the possibility of energetically exciting the wavepacket. So, you can never be sure how much your first measurement just before the barrier affected the result of your second measurement after the barrier.

Furthermore, if you want to try to measure the wavepacket while it is inside the barrier (or any other classically forbidden region), your measurement technique will necessarily involve the possibility of exciting the system such that it's total energy is no longer below the barrier. So, you will "see" the wavepacket, but you won't be able to say anymore that it is "inside" the classically forbidden region, because it could be in an energy state "above" the classically forbidden region.

 

[ZapperZ]

In quantum tunnelling,as I understood,when a particle reaches the boundry of a potential barrier,it is possible,that the particle passes the barrier and it is performed like disappearing before the barrier and appearing after it.If the latter is the case,so there should be a motin which is faster than light.But it can't be correct.

Your starting premise is faulty.

The particle doesn't disappear in the barrier. There is a finite, non-zero probability of finding the particle in the barrier. In fact, in superconducting tunnel junction, if I put magnetic impurities in the barrier, I can affect the tunneling properties easily! This clearly show that the particles that are tunneling interacts with that's in the barrier, and thus, passes through it!

Zz.