Part of the Casswiki article series Natural science
Quantum Tunneling can be defined as:
a) A quantum leap through a barrier.
b) A process by which a quantum system can suddenly and discontinuously make a transition from an initial configuration to a final one, even if the system does not have enough energy to classically attain the configurations between the two.
c) Feature of quantum mechanics showing that objects can pass through barriers that should be impenetrable according to Newton’s classical laws of physics.
Regarding the definitions given above, the following (simplistic) example may help to clarify. Let us say we are bouncing a ball on the ground with less force then it would take for it to reach escape velocity and bounce into outer space (I told you it was simplistic).
When the ball reaches its highest point, just before it stops in midair to fall back to the earth, its kinetic energy (it’s energy of motion) would then be at minimum (zero) and its gravitational potential energy (it’s stored energy) would then be at maximum. This is because as the ball’s kinetic energy decreases its potential energy increases. The greater the kinetic energy of the ball then the less its potential energy and vice versa. So at its highest point the potential energy of the ball went to maximum while it’s kinetic energy went to minimum (zero).
Now, the total energy of the system is the sum of it’s potential and kinetic energy values (Total Energy= KE (Kinetic)+ PE (Potential)
So, at this point, if the ball were to mysteriously “quantum jump” or “leak through” the potential barrier of the gravitational field of the earth and fly off into space, then it would have to go through a place or reach a “pedestal” within this barrier where it’s potential energy was greater than its total energy.
But yet, its Total Energy would not change…see equation above.
In other words, if the potential energy of the ball had to increase to get to that “pedestal” point, and if the total energy of the system still stayed the same, then its kinetic energy value would have to go into the negative region since the kinetic energy was at zero when it reached its highest point. It’s kinetic energy would have had to go more negative to “balance the equation” when the ball “jumped” to a higher potential energy state.
However, this would contradict the laws of classical physics since its kinetic energy can’t be negative.
Kinetic energy can be defined as the energy of motion. Any object that moves has some energy due to the fact that it is moving. This energy is equal to half of the object mass multiplied by its velocity squared. Since mass and velocity squared are never negative, kinetic energy is also never negative.
So clearly if the ball were to suddenly appear on the opposite side of the gravitational field and fly off into outer space, it would have had to have broken through a potential energy barrier where its kinetic energy value went into the negative region and that would be impossible since kinetic energy cannot be negative within the laws of classical physics.
So this is clearly impossible, at least from the standpoint of classical physics.
But not Quantum mechanically. When the ball or ‘particle’ is now of subatomic size, and behaves in accordance with Quantum mechanical laws, then the ball’s position has now become more uncertain and its position now kind of spreads out into waves. I guess they could be called “matter waves.”
Mathematicians and scientists, such as Schroedinger, deBroglie, and Einstein, have advocated a wave structure of matter. Quantum mechanics only requires that the total average energy summed up over all possible positions of the particle be equal to the total average energy. It’s OK to have a negative kinetic energy at some point as long as it’s balanced by a positive contribution somewhere else. Thus the Quantum particle is allowed to visit “classically forbidden” regions of the potential energy barrier, i.e., those inside the pedestal when the top of the pedestal exceeds the total energy. However, the wave function is greatly damped in these regions, and more so as the top of the pedestal is raised further, indicating that the probability of the particle being in a classically forbidden region is greatly reduced.
Thus the wave can leak through a region where the potential energy is actually bigger than the total energy. Once it’s leaked through, part of the wave can be out somewhere else, such as on the other side of the potential energy barrier.
If the position of the wave is truly spread out, not just hidden or unmeasured, it’s raw uncertainty allows for the wave function to penetrate the barrier. This is genuine indeterminism, not simply an unknown quantity until someone measures it.
The process used to explain this crossing of the barrier phenomenon is called Tunneling. Tunneling is a process by which the “particle wave” or “matter wave” tunnels through (or makes it’s way through) the potential barrier to the other side and the probability term that describes this event is called the Tunneling Coefficient.
However, something tricky happens. When the wave interacts with other things, for example when try to view it in a microscope, it quits acting so spread out, and you find the particle in some region or other. (We don’t really understand this process. ) Usually you find it in regions where the wave is large.
So, the particle can start out ‘trapped’ yet later show up outside the trap. We say it tunneled out.