Quantum Mechanics is all about probability. If there's a certain probability or an event that can't be pursued in our macroscopic life it is simply terminated . But things get weird in quantum mechanics and yes it does follow the probability of occurrence. As it is fully developed on theories and probability we can't neglect the weird ideas on results. Similarly, quantum tunneling is also a same concept where probability plays a great role.
Before understanding quantum tunneling we must understand some basic information about maxwell equations and properties of light which gave ideas of quantum tunneling.
Tunneling is further developed according to Maxwell theory about light reflection and his equation. Maxwell equations were generalized for wave meaning those equations had given us some function about waves. Since light is also an electromagnetic wave it does follow Maxwell equations.
( The evanescent wave leaves the box)
As light is an electromagnetic wave which follows Maxwell equations and by solving those we get a weird result as compared to our classical physics.
We know,
When light enters a medium it gets reflected and if at certain angle light gets fully reflected then that process is called a total internal reflection.We're taught in classical physics about Total Internal Reflection that how light is completely reflected under certain angle.
But, when we use the Maxwell equations on light as being a electromagnetic wave, we found something intriguing called an
EVANESCENT WAVE.
This is an evanescent wave which was found on Maxwell equations. This was very weird because in classical physics we didn't found it but while solving Maxwell equations it was found that some part of light was leaking. Since, it was first proved theoretically it was ignored but later it showed some impacts. So light doesn't get reflected totally, some part of it leaves and quickly fades. In classical physics it is simply not concerned because it simply fades. But sometimes the evanescent wave doesn't fade and again gets reflected this is called frustrated total internal reflection. This reflection occurs when the evanescent wave is at certain angle with the other reflecting mirror and gets reflected again and hence doesn't fade away quickly. It is also proved experimentally that light as an electromagnetic wave follows Maxwell equations and causes evanescent wave and can create multi reflection.
If you're wondering what Maxwell equation is
The exponential present there indicates the direction.
We can plot the graph of that exponential and gain it's direction .
Evanescent waves are observed experimentally it can be somehow observed on labs with simple equipments causing frustrated total internal reflection.
Ok, now we know that waves can be diffracted from a medium just like a evanescent wave. So let's say if a particle has a dual nature of both wave and a particle then it must follow Maxwell equations and should cause evanescent wave just like the light and that is Quantum Tunneling. According to De Broglie every matter is associated with wave. In fact in quantum mechanics everything like the electron and other fundamental particles are both wave and particles. When we observe things it changes its property. When an electron is in a box and we don't observe it , it is in superposition state which means it is both wave and particle at the same time but if we open the box the wave function collapse and particle is seen. This is related to Schrödinger Cat experiment ( I'll explain it briefly in another blog.)
So let's say there is a electron in a box and we don't observe it. Remember if we don't observe a electron then the electron is in a superposition meaning it can be wave and a particle so the probability of that electron before we observe could be anywhere we can't decide the exact position of electron without opening the box we can only guess the where the electron is likely to be and hence the wave function is spread out like a wave.
But when we open the box that probability is change so the wave function (function of wave, where the electron is most likely to be) is certain and it collapses forming a particle with fixed position.
Quantum tunneling exactly works like that similar scenario. When an particle is in a box and not observed then it acts as a wave and hence follows Maxwell equations. So if we solve those equations we will get evanescent wave which was mentioned above. Since evanescent wave can leave the box by causing total internal reflection then the electron also have some probability to be outside on the box when it is a wave.
So when a particle is inside a box and we don't observe it then it can be anywhere and there is slightly a non zero probability that the particle may be outside of the box too since it acts as a wave and creates evanescent wave.
