Quantum Tunnelling: Where Does Energy Go?

[mrcotton]

Homework Statement

The waves amplitude appears to decrease as it tunnels through the barrier.
If we think of the amplitude as energy like in a sound wave etc, where does this energy go?

The Attempt at a Solution

I think it has something to do with the fact that for a matter wave the amplitude has no interpretation and that it amplitude squared is the probability of finding it in a location. So this will decrease through the barrier until it exits on the other side at that point it represents the probability of it being at that point?

Incidentally the electron does not move through the barrier?

Thanks for any clarification or further mystery

 

[BruceW]

yeah, the amplitude of the wave is only telling us about the probability of finding the particle in that position. But you are also correct that we can interpret this amplitude as related to the energy of a beam of particles. Think about the case where we have a bunch of similar, but non-interacting particles, all with this same wavefunction. Why will we expect a detector to receive more energy in places with a large amplitude for the wavefunction?

 

[mrcotton]

would this be because if there is a higher probability of finding more particles in a particular location then there must be more energy concentrated there. Would this be there kinetic energy detected by the detector?

Thanks for responding

 

[BruceW]

yeah, that's it. It just means that on average, there is going to be a lot more particles there, so if there are N particles, each with energy E, then the detector will pick up a total energy of N*E (well, the detector might not necessarily pick up all the energy of each particle, but this does not change the main idea of the argument).