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What is this mysterious quantum tunneling effect, where does it come from? And why is it one of the most important phenomena in physics?
Quantum mechanics shows that quantum objects have a wave-particle duality. What we think of as an electron particle actually behaves like a wave, a probability wave. This means that its position is not a precise location in space. It is defined by a wave function that can only tell us the probability of finding it a particular location when measured. The wave function of a particle exists in all of space, in the entire universe up to infinity. So there is always a non-zero probability of finding the electron anywhere, including outside a barrier.
We can attribute this behavior to the Heisenberg uncertainty principle. It states that the uncertainty in a particle’s position times the uncertainty in its momentum has to be greater than a finite number. Practically this means we cannot know with 100% certainty what the position of that electron is. And the wave function of the electron, which gives us the probability of finding it at any location can be found using the Schrodinger equation.
This equation was developed by Erwin Schrödinger in 1926, and it is the equation that describes the wave nature of matter. The Greek letter psi in the equation is the wave function. The wave function depends on both time and position. It can be both positive or negative, but the square is always positive. The square of the wave function as a function of position is the probability of finding the particle at that position. The Schrödinger equation is a statement of conservation of energy. It says that kinetic energy plus potential energy equals the total energy—But instead of just energies, we have energy operators acting on the wave function of the particle.
For a particle inside a box with a wall of finite thickness and height, we can solve the wave function inside the box, in the barrier and also outside the barrier. We find that the amplitude is non-zero within and outside the barrier. So, it can has some probability of being outside the box.
This doesn’t work for large objects like a tennis ball because the wave function depends on several factors, like the thickness & height of the barrier, and the mass of the particle. For macro size objects, the mass is so large, and the thicknesses of the barriers so great that the wave function will have an extremely small value, making the probability extremely small.
If you do a rough calculation for my hand to tunnel through the wall, the probability is about 10^-40 – more zeros than atoms in my body (10^28). This is statistically though not physically impossible.
Tunneling has huge implications in nature and technology. For example, transistors in electronic devices have a source on one side, and a gate to control the flow of electrons to the drain on the other side. If the gate is too thin, the electrons just tunnel straight though, ruining our circuit. This is why transistor can’t get much smaller, which is a roadblock for developing better electronic devices.
#quantumtunneling
Quantum tunneling is responsible for the sun shining. Stars shine due to nuclear fusion. The sun fuses the nuclei of hydrogen atoms together to form helium. Tunneling is essential because hydrogen nuclei composed of positively charged protons repel each other. In order for them to come together, they have to overcome this extremely strong repulsion, called the coulomb potential. Because of quantum tunneling, the probability for this process to occur, becomes much more likely because the two nuclei can tunnel through this barrier. If it weren’t for quantum tunneling, most stars may never have ignited.
The universe itself may have come to be because of Tunneling. The big mystery is what gave the big bang the kick that it needed in order to overcome the energy required to counteract attractive forces like gravity.
This is not well understood, and not proven, but according to calculations made by physicist Alexander Vilenkin, the probability that the universe could overcome the energy barrier needed for inflation to occur and the big bang to result, is not zero even at the limit of the universe being size zero – that is having no space and no time – a universe from nothing!
