Quantum tunnelling

[hobz]

I fail too understand what properties of Nature are responsible for getting particles (representing energy) out of a local energy state minimum to an absolute energy state minimum.

 

Perhaps it is not fair to demand an explanation of the ways of Nature. In that case, what logic explains the act of tunnelling through a potential barrier without having the energy to do so.

 

Are the responsable mechanics related to the spontaneous nature of atom emissions and absorbsions?

 

Where does the lost energy go?

[Klaynos]

This is a bit handwavey, and not perfect but....

 

 

Into the barrier the probability wave function decays, this is a result of solving shrodingers equation using sensible boundry conditions. If this decay is long enough, and the barrier short enough there can be a significant part of the probability wave function outside the barrier, meaning there is a chance that the particle exists outside the barrier.

[Xittenn]

This is a bit handwavey, and not perfect but....

 

 

Into the barrier the probability wave function decays, this is a result of solving shrodingers equation using sensible boundry conditions. If this decay is long enough, and the barrier short enough there can be a significant part of the probability wave function outside the barrier, meaning there is a chance that the particle exists outside the barrier.

 

So what you are saying while waving your hands is something like........the electrons in a transistor which want to pass over the base/emitter boundary for the most part fall under the potential barrier which restricts. But, because the electrons energies fall within a probability distribution some may have the energy to overcome this barrier and do? Under the 'appropriate' conditions...............I always wanted to truly understand Quantum Tunnelling yet never took the time to look at it!

Edited February 6, 2009 by buttacup

[swansont]

Where does the lost energy go?

 

What lost energy?

 

As long as you wait for a time [math]t > \frac{\hbar}{E}[/math], energy will be conserved.

[hobz]

The loss in potential energy of the particle.

Emitted as photons?

[swansont]

The loss in potential energy of the particle.

Emitted as photons?

 

Depends. In alpha decay there often isn't a photon. The energy appears as kinetic energy of the alpha and the daughter.

[hobz]

Does your time criterium imply that quantum tunnelling can happen over infinite distances of potential barriers, as long as we "wait" long enough?

[swansont]

Does your time criterium imply that quantum tunnelling can happen over infinite distances of potential barriers, as long as we "wait" long enough?

 

It means the longer you need to tunnel, the lower the barrier can be.

[CPL.Luke]

yeah an easy way to think of it in general (and also a very good approximation) is that the wave function for a given energy level decays exponentially in the region E<V meaning the probability density of the particle in the region E<V is going to fall off pretty rapidly, however there is a chance if the region E<V is short and returns to a region where E>V that we'll see the normal oscillatory wave functions, now if we have a particle with a given energy, it can be anywhere and we can't really speak of it being on one side or the other, until we measure where it is.

 

now if we localise the wave function to one side of the barrier, and then let it evolve for a little time, it will spread, and this spreading should result in some probability that the particle is on the other side of the barrier.

 

there is a pretty good visualiser for various quantum potentials here.

 

http://www.falstad.com/qm1d/

 

play around with the step potentials a bit and you'll see whats happpening, the key thing is that in these systems you can't measure energy and position at the same time. If I measured a a particles position and it was inside the high potential area, then the particle had the energy to be there, and if I measured the particle somewhere else the same thing occurs, and if I measure the energy I know very little about where the particle is.