How does quantum tunneling work?
As previously stated, on the macroscopic scale (the scale at which objects are large enough in size to be seen by the naked eye), if the object which in this case is a ball of mass m is moving with a kinetic energy k up a hill, the kinetic energy would need to be higher than the potential gravital(the height) in order for it to go over the hill.
K < U = mgh
k=Kinetic energy.
U=Potential energy.
mgh= Potential energy due to gravity. (m=mass of object) (g=acceleration due to gravity) (h=height of the object)
K < U = mgh
k=Kinetic energy.
U=Potential energy.
mgh= Potential energy due to gravity. (m=mass of object) (g=acceleration due to gravity) (h=height of the object)
Particles at microsopic scale
At the microscopic scale at which quantum tunneling occurs, particles (in this case an electron) act different compared to classical mechanics in the macroscopic scale. In the quantum world particles exhibit a wave-like nature. They often act like waves of water as opposed to billiard balls. What this means and what really allows quantum tunneling to occur is that an electron does not exist in a single place at a single time as well as having just a single energy. Instead it exist as a wave of probabilites. According to Quantum Mechanics, there is a non-zero probability that when a particle is able to tunnel through a barrier. Even if the kinetic ( or electric energy) is less than that of the potential barrier.
At the microscopic scale at which quantum tunneling occurs, particles (in this case an electron) act different compared to classical mechanics in the macroscopic scale. In the quantum world particles exhibit a wave-like nature. They often act like waves of water as opposed to billiard balls. What this means and what really allows quantum tunneling to occur is that an electron does not exist in a single place at a single time as well as having just a single energy. Instead it exist as a wave of probabilites. According to Quantum Mechanics, there is a non-zero probability that when a particle is able to tunnel through a barrier. Even if the kinetic ( or electric energy) is less than that of the potential barrier.
The image shown of the right is a diagram of a particle and an electron (with wave-like characteristics) tunneling through a potential barrier
Tunneling particle/electron
From the the top image we can see the particle/electron (blue circle) encountering the potential barrier which in the microscopic scale is an electric field. According to classical physics the particle should be repelled by the potential barrier and move in the opposite direction. But in quantum mechanics what actually happens is that the particle has a probability of tunneling pass the potential barrier and reaching the otherside of the barrier.
From the bottom image, we can see that the particle being at a microscopic scale has the form of a sinusoidal wave. When the wave begins to penetrate the potential barrier, the function of the wave beings to decay at and exponential rate. Just before the sinuoidal wave decreases all the way to zero, it exits/resurfaces from the barrier out to the other side, but with a smaller amplitude than that it had at the start. The reason for the decrease in amplitude is due to the fact that not all of the particle tunnelled through the barrier. Parts were repelled by the barrier and moved in the opposite directions, while others are actually stuck inside the barrier.
This movement of the particle pentrating barriers is the phenomenon known as
Quantum Tunneling
From the the top image we can see the particle/electron (blue circle) encountering the potential barrier which in the microscopic scale is an electric field. According to classical physics the particle should be repelled by the potential barrier and move in the opposite direction. But in quantum mechanics what actually happens is that the particle has a probability of tunneling pass the potential barrier and reaching the otherside of the barrier.
From the bottom image, we can see that the particle being at a microscopic scale has the form of a sinusoidal wave. When the wave begins to penetrate the potential barrier, the function of the wave beings to decay at and exponential rate. Just before the sinuoidal wave decreases all the way to zero, it exits/resurfaces from the barrier out to the other side, but with a smaller amplitude than that it had at the start. The reason for the decrease in amplitude is due to the fact that not all of the particle tunnelled through the barrier. Parts were repelled by the barrier and moved in the opposite directions, while others are actually stuck inside the barrier.
This movement of the particle pentrating barriers is the phenomenon known as
Quantum Tunneling