When a particle tunnels where does the energy come from

[matt_crouch]

when a particle tunnels where does the energy it "borrows" come from.

 

[HallsofIvy]

In what sense does it "borrow" energy?

 

[ice109]

he's not talking about tunneling, he's talking about virtual particle anti-virtual particle creation annihilation.

 

[jambaugh]

when a particle tunnels where does the energy it "borrows" come from.

There are a couple of ways of looking at tunneling. You could say you "borrow" energy from vacuum fluctuations but that's not really right.

Another way to look at it is that energy barrier it being described classically when quantum mechanically moving toward the barrier is an increased likelyhood of absorbing a (virtual?) boson and being kicked back. Classically such "kickbacks" are happening continuously but in QM they are statistical, somewhat like the force of pressure due to particles bouncing off an area. In this picture what's happening is the particle is "slipping past the guards" occasionally without actually interacting with the source of the barrier potential.

There are problems with this picture as well but I like it better and it eliminates the need to "borrow energy". The particle just needs to be "lucky" enough to "sneek" through the barrier without being caught and pushed back.

 

[LURCH]

I think he is talking about quantum tunneling. The idea of quantum tunneling is that a particle "jumps" across a barrier that it could not cross if it were a classical particle. Specifically, the particle crosses a barrier which it should not have the energy to cross.

According to http://www.colorado.edu/physics/phys2130/phys2130_fa06/feedback/feedback_wk10.htm" from the University of Colorado, this energy appears to be borrowed from the ZPE:

Radioactive decay is basically alpha particles tunneling out of the nucleus. The amount of time an electron spends in an excited state is a little more subtle, but it has to do with the fact that if there are no photons around, an electron really should be stable in an excited state, but it “borrows” energy from the vacuum to get out of the excited state.

[I type slower than Jim Baugh]

 

[matt_crouch]

Sorry Halls Of Ivy i was a bit vague with my question in the sense that LURCH describes it... i did mean quantum tunneling. where a particle meets a barrier and seems to pass straight through it without lossing energy ( i think it doesn't loose energy)

the analogies i heard was that it was like throwing a stone at a piece of glass and expecting it to bounce back but it passes straight through.

Or instead of work being done to climb a hill it passes straight through. That's where i got the "borrowing" energy.

how can a particle borrow energy from a vacuum?

 

[matt_crouch]

sorry i wasnt meant to say that i meant tunneling in the way that LURCH described it.

 

[Vanadium 50]

There is a great temptation to describe quantum mechanics as "just like classical mechanics except..." and then to provide some sort of ansatz or analogy. The problem is that QM isn't "just like classical mechanics except..." It's quite different, and eventually these kinds of shortcuts end up leading one astray.

Tunneling is not well explained by this idea of borrowing energy. In particular, it doesn't explain why the thickness of the barrier matters, rather than just the height, and it sure doesn't explain why there are cases where a slightly thicker barrier actually increases the tunneling.

I would chalk this up to stretching an analogy beyond where it's useful.

 

[ZapperZ]

I concur with Vanadium. In elastic tunneling, there's no change in energy of the particle that tunneled though. So what energy did it borrow? It doesn't need it to tunnel because the wave function and the boundary conditions ensures that there is a "penetration" of the particle into the classical forbidden region. So where's the extra energy needed here?

The standard treatment of elastic tunneling has no "borrowed" energy. Look at the Hamiltonian for a tunneling process if one doesn't believe that.

Zz.

 

[waht]

By the Heisenberg uncertainty principle, a particle is spread out in space in its position and momentum as a wave of probability. The electron didn't tunnel through the barrier, rather by the superposition principle, it could have existed inside or outside the potential barrier. Only a measurement will tell you its state, otherwise it could exist in both states simultaneously.