If we look at the world from the perspective of microscopic particles, our surroundings will become very different, because all the matter around us will be presented in the form of atoms and neutrons, and generally we think of electrons and neutrons, protons and ions below electrons as microscopic particles. It may be clearer to say this: we divide the material world into two scales, and the well-known solar system, the Milky Way and other celestial bodies exist in a space called the large universe; and the smaller microscopic world of particles, electrons or neutrinos that cannot be observed by the human eye is called the small universe.
If the big universe is the biggest display stage in the whole world, then the small universe is the more mysterious Pandora's box, which hides many microscopic particles of all kinds. Whatever the difference, they are one of the most important parts of the world, after all, when we are accustomed to the dazzling starry sky, turn around and look at the deeper microscopic particle world, will it be more shocking?
Many people feel that these microscopic particles are very difficult to talk about, coupled with their lack of understanding, it is easy to have boring ideas about these theories and turn their eyes to the grand universe. In fact, the microscopic world is equally interesting, each atom is a "solar system", the nucleus is like the sun, and the neutron and electron are the "planets" that orbit the nucleus. There are also many interesting phenomena in the microscopic world, such as the need to follow the Pauli principle in the arrangement of electrons outside the core of atoms, and the electrons outside the nucleus will occupy the lowest-energy orbit first, and then travel to the high-energy orbit in turn. Taking oxygen atoms as an example, even if there is no slightest difference between these electrons, you can see their neatly arranged side, like a group of obedient children sitting in seats, and only the current row can sit in the last row when it is full.
Not just atoms, Pauli's principle follows even neutrons and protons, and proposes an almost general law: no two electrons in an atom can have the same quantum state. We can understand this as the arrangement of electrons around the nucleus of an atom is spiraling, and the latter electron state of each electron is a little higher, tightly arranged and at the same time neatly arranged, as beautiful as the rotating arms of the Milky Way.
Pauli's principle is one of the most important fundamental theories in quantum mechanics, which explains that when two arbitrary particles in an atom are swapped at their positions, their wave functions will be completely antithetical. Since this symmetry was thought to be two particles with exactly the same quantum states at an earlier stage, but we can see from the order of electron arrangement outside the nucleus that there will be no particles with the same quantum state in an atom, Pauli's principle solves this problem.
So what is the use of Pauli theory? In layman's terms, it has almost no role in life, just like trigonometric functions in mathematics, Pauli theory is only a principle, a most basic proof. But it plays a huge role in quantum mechanics, a role we cannot describe in words, with the help of Newton's metaphor is "we are just standing on the shoulders of giants", if you have to evaluate Pauli theory, it may be the "giant".