Quantum Tunneling

In this blog, I am going to write about what according to me is the most fascinating phenomenon in the quantum world: Quantum Tunneling.

For now, let us consider an analogy about classical physics.
Imagine throwing a ball at a wall(barrier) as shown in the diagram on the left. According to classical physics, the ball will bounce off the wall and come back to you(assuming its kinetic energy is not high enough to break the wall) and this is the only possibility.
Does this concept apply similarly to Fundamental particles?
How does quantum physics(the study of fundamental particles) account for this?

On the first hand, if you have read my blog about wavefunctions, you must surely know that the probability distribution of electrons can be determined using the electron's wavefunction(an example shown in 2-D below).

Moreover, the electron possesses a wavefunction owing to its wave-particle duality.
The highest probability of finding the electron is at the highest amplitude and probability decreases with decreasing amplitude.
Even at a very low amplitude, there is an infinitesimal probability of finding an electron
This stipulates that whenever there is a wavefunction(non-zero amplitude), there is a probability of finding an electron.


Now let us visualize an electron moving towards a potential or electric barrier, like a wave and possessing a wavefunction. As it hits the barrier, according to quantum physics, there are two possible outcomes: it either reflects back or it passes through the barrier!!!
The event of passing through the barrier is known as quantum tunnelling.

Let me elaborate further on this matter of concern.
Whenever a wavefunction hits a potential barrier, the wavefunction decays exponentially inside the barrier. If the barrier is thick enough(very high potential energy), the electron will bounce back as shown in the diagram on the left because its wavefunction has decayed to a zero amplitude inside the barrier. (green dots=wavefunction, red sphere=assumption of the position of the electron)

But what happens if the barrier is thinner and has a reasonable potential???
As the wavefunction hits the barrier, it will decay exponentially as it did for the thicker barrier(high potential) but the difference will be that it will decay to a non-zero amplitude and after leaving the barrier, it will continue to exist, but at a shorter wavelength.
And in this game of probability, as already explained, whenever there is a wavefunction(non-zero amplitude), there is a probability of finding an electron and hence the electron can be found on the other side of the barrier.
This classically forbidden phenomenon is known as Quantum Tunneling and this diagram below sheds more light on it.




Wavefunction 1(Ψ1) is the original wavefunction of the electron. Ψ2 is the exponentially decaying wavefunction inside of the potential/electric barrier. Ψ3 is the wavefunction leaving the barrier with a smaller amplitude.

This is how an electron tunnels across a potential barrier. This does not happen all the time because it also somehow depends on the kinetic energy of the electron but depends more on the width of the barrier.



The thinner the barrier, the less will the wavefunction decay and hence the wavefunction leaving the barrier will have greater amplitude and therefore, chances of tunnelling increases,
And the most preponderant thing to be bent on is that it is all a game of probability.

Now let's indulge in areas where the event of quantum tunnelling may be observed.
Stellar fusions

Let us take for example the sun, where there is the nuclear fusion of hydrogen protons to form helium and other heavier atoms. Theoretically, if we would have to perpetuate the same reaction on Earth, we would need to heat up hydrogen a hundred times the heat of the sun to be able to fuse them. This is because it is actually really hard to get two protons(same charge) to come close to each due to the Coulombic repulsion.
The protons must, therefore, possess a huge amount of kinetic energy to overcome the repulsive force which is very rarely sufficient.
Well, one theory states that the sun having the mass of 99.8% of the whole solar system, has an unimaginable gravity and this is what fuses the hydrogen together.
Another theory is the advent of quantum tunnelling. Due to the lack of kinetic energy to break the Coulombic repulsive energy(the barrier) and also that protons possess wave-particle duality(hence have a wavefunction), it was deemed by scientists that the protons may tunnel through the imposing barrier to be able to fuse.

Smell receptors
Initially, it was believed that the nose worked by the lock and key process, meaning that odour molecules(key) get trapped by chemical receptors(lock) and according to the structure of the molecule, a signal is triggered in the brain.
But what happens for ethanol and ethanethiol, where both have nearly similar molecular structures. (shown below)

Ethanol is the alcohol that human consumes while ethanethiol is the odour of rotten eggs.
Hence how does the human body differentiate between these smells???
Well, a plausible theory concluded by scientists was again the advent of quantum tunnelling.
It starts with this:
Chemical receptors pump a small current to the odour molecule, causing it to vibrate(molecular vibration) and these molecular vibrations are characteristic. For the current to flow, there must be a flow of electron which is classically impossible because of the non-conducting gap between the molecule and the receptor. The electron is thought to tunnel through the gap to the molecule.
Experiments with molecules having lots of hydrogen have been used due to its high vibrational frequency and positively, these results have shown an increase in quantum vibrations. These also initiated that humans are capable of differentiating between different molecular quantum vibrations.

Why hydrogen? (according to my analogy)








According to the above equation, the frequency of vibration increases as the reduced mass decreases. The mass of hydrogen is very low and hence has a high vibrational frequency.
The reduced mass is the inertial mass: that is the mass of two atoms in a molecule acting as a single mass. Reduced mass is calculated as follows:

k, the force constant is the stiffness of the bond.

Other uses of quantum tunnelling are Scanning Tunneling Microscope, Tunnel Diodes .....

I hope that this concise explanation about quantum tunnelling was well informative and that it raised your awareness about the mysteries of the quantum world.
If you wish to add to your pool of knowledge, click on the link below.
https://www.theinfinitypost.com/