Quantum Tunneling and Energy

During quantum tunneling, I have heard that a particles 'borrows' energy from the 'barrier' to drift through it and returns it back after a certain time period. How important and common is this and how do you calculate the energy losses occurred during the process?
- Vishakha LS (age 16)
Shimoga, Karnataka, India

Here's an old description of tunneling: .

I'm not sure what it means to say that the particle " 'borrows' energy from the 'barrier' ". It seems cleaner to think of it directly in terms of the quantum wave. When the wave is in a region (the barrier) where the potential energy is larger than the total energy, the solution doesn't have to be zero. An exponential shape gives the a negative local part of its kinetic energy, rather than the positive part that comes from twisting around in the complex plane. So that leaves a tail of the state outside the barrier.

There aren't really "energy losses" in this process by itself. The particle ends up with the same net energy it started with. To get any losses you'd have to have some coupling to something else that could take up some energy, such as internal vibrations in whatever provides the barrier.

Quantum tunneling is extremely common. It's involved in many electronic devices (e..g. tunnel diodes) and in radioactive decays. Perhaps the most important type for our daily lives is the quantum tunneling step that allows nuclear fusion to power the Sun.

Mike W.

(published on 04/25/2014)