Explain quantum tunneling to me in detail provided I have some physics knowledge from university
Quantum tunneling is a phenomenon in quantum mechanics where a particle can pass through a potential barrier, even if the particle's energy is less than the potential energy of the barrier. This is because, at the quantum level, particles have wave-like properties and can exhibit wave-like behavior, such as diffraction and interference.

To understand quantum tunneling, let's consider a simple example. Imagine a particle, such as an electron, is traveling towards a potential barrier, such as a wall. In classical mechanics, the particle would not be able to pass through the wall if its energy is less than the potential energy of the wall. However, in quantum mechanics, the particle can have a wave-like nature that allows it to "tunnel" through the wall.

The reason for this is that the wave function of the particle does not abruptly go to zero at the barrier, as classical mechanics would predict. Instead, the wave function of the particle has a small, non-zero value on the other side of the barrier. This means that there is a small probability that the particle will be found on the other side of the barrier, even if it does not have enough energy to overcome the potential energy of the barrier.

The probability of the particle tunneling through the barrier is related to the thickness and height of the barrier, as well as the energy of the particle. The lower the energy of the particle, the lower the probability of it tunneling through the barrier. However, even particles with very low energies can still tunnel through barriers, given a large enough number of attempts.

Quantum tunneling has many practical applications in physics and engineering. For example, it is used in the design of tunnel diodes, which are used in electronic circuits to generate high-frequency signals. It is also used in scanning tunneling microscopes, which are used to image surfaces at the atomic scale.

In summary, quantum tunneling is a fascinating phenomenon in quantum mechanics that allows particles to pass through potential barriers, even if they do not have enough energy to overcome the barrier. It is an important concept that has many practical applications in physics and engineering.