h2g2 The Hitchhiker's Guide to the Galaxy: Earth Edition

Quite a nice introduction.

But the picture with the roller coaster is still much too simple because tunnelling still exists if the energy is *definitly* under the barrier energy, meaning that the roller coaster is too slow to reach the top for sure. In calculations one discrete energy is assumed, and still tunnelling takes place.

The tunnelling effect is caused by the fact that impulses and thus velocities can be imaginary leading to some kind of negativ kinetic energy. These leads to a finite probability for the particle to be at the classically fobidden region.

But I think your explanation is still more suitable than mine. One has to know the problem quite well (with all the mathematics) to understand what I mean.

By the uncertainty principle, what happens if you know the energy precisely? Don't you lose all knowledge of the time-location of the particle? In which case you wouldn't be able to tell if it had tunneled or not.

That's quite a good question.

If you know the energy precisely, the system is static, that means, that nothing is going to change for all time. Anyway, a river doesn't change in time, too, but there is quite a huge amount of water carried down through the time. In time-independent quantum-mechanics you can still have a flux of particles. And there is still non-zero flux in classically forbidden regions if tunnelling is in effect.

Measurement is some really strange kind of thing which destroys all the balanced things of what was known before, and which cannot be known. This means that, even if you cannot know something, you are still able to measure it, taking a loss of something that was known before.