Quantum mechanics

Quantum mechanics is a fundamental theory about how the world works. It describes the behavior of matter and light. This theory is most useful for things at a very small scale. These are things like atoms and subatomic particles.

At this tiny level, the rules of the world change. Normal physics, called classical physics, works for big things we see every day. However, classical physics is not enough to explain the submicroscopic world. Quantum mechanics fills those gaps by showing us how tiny particles behave. It is the foundation for many other sciences, like quantum chemistry and quantum biology.

How does this tiny world work? It works using probabilities instead of certainties. In our world, we expect to know exactly where a ball is. In the quantum world, we use a wave function to find out what might happen.

A wave function is a math tool that gives us probability amplitudes. These amplitudes tell us the chance of finding a particle in a certain spot. A scientist named Max Born created a rule called the Born rule to explain this. By using his rule, we can find a probability density function. This tells us where an electron is most likely to be found. We cannot say for sure where it is, only where it might be.

Scientists built this theory over many years. It began with ideas that did not fit with old rules. In 1900, Max Planck found a solution to the black-body radiation problem. Then, in 1905, Albert Einstein wrote a paper about the photoelectric effect. He showed how energy and frequency are linked. These early ideas were called the "old quantum theory." Later, in the mid-1920s, the full theory was developed. Many important people worked on this, including Niels Bohr and Erwin Schrödinger. Other scientists like Werner Heisenberg and Paul Dirac also helped build it.

There are many strange facts in quantum mechanics. One is called wave-particle duality. This means light and electrons can act like both waves and particles.

Another idea is the uncertainty principle. This rule says we cannot know a particle's exact position and its momentum at the same time. There is also a thing called quantum tunneling. This lets a particle cross a barrier that it should not be able to cross.

This process helps stars perform nuclear fusion. Even particles can become entangled. This means their properties are linked together in a special way.

These tiny rules connect to the big world in many ways. Quantum mechanics helps us understand how stars shine through fusion. It also explains how certain electronic parts work. We use these ideas in things like scanning tunneling microscopy. Even though it seems strange, these predictions are very accurate. For example, quantum electrodynamics can predict electron properties with amazing precision. It is accurate to within 1 part in 10 to the 12th power. This shows that even if the rules seem odd, they are true.