Is the principle of strong degeneration and lower Pauli invalid 5

Pauli's principle says that each orbital (e.g. 1s orbital, px in 2p orbital) can only hold a maximum of two electrons with opposite spins. Hunt's rule states that in orbitals of the same energy, electrons preferentially enter empty orbitals when they are arranged, and single electrons in each orbital acquire the same spin.

For example, there are three 2p orbitals, and now there are four electrons to be filled, the first three electrons each occupy an "empty seat", and the last electron will either go to the 3s orbital to find an empty seat, or "squeeze" with the electrons in the 2p orbital (which will be slightly higher than the energy entering the empty orbital). This electron eventually found that it was more comfortable to squeeze with others (lower energy), and it seemed that it didn't have the ability to run to 3s (I didn't have enough energy). The electrons are always arranged in a way that satisfies the principle of lowest energy, as well as the Pauli principle and the Red rule.

Another example: there are 7 electrons outside the n nucleus, the electrons first fill the 1s orbital (the orbital has the lowest energy, the priority arrangement, the two electrons spin opposite, and the two arrows are one positive and one negative) and then fill in 2s (the orbital energy is the second lowest, and the 2 electrons spin is opposite), and then fill in 2p (the remaining three electrons each occupy a p orbital, the three electrons spin the same, each electron uses an arrow, the three arrows are in the same direction, up or down).

Boltzmann statistics is a semi-classical theory. Strong degeneracy refers to the fact that one energy level corresponds to many states, but each state can still accommodate only one electron, so it still follows Pauli's principle of incompatibility.

Different fermions follow a principle of Pauli incompatibility between particles, and the forces generated by the principle may belong to different roles. For example, the electron degenerate pressure is an electromagnetic interaction, whereas the neutron degenerate pressure is a strong interaction.

Quoted from the Chinese Wikipedia entry "Electronic Degeneration Pressure".

The electron degeneracy pressure is a force generated by Pauli's principle of incompatibility, which illustrates that two fermions cannot occupy the same quantum state at the same time, and this force is also the limit of what matter can be compressed. In stellar physics, this is an important quantity, as it is responsible for the existence of white dwarfs.

Here is the Dirac constant (reduced Planck constant), δx is the uncertain value at position at the time of measurement, and δp momentum measures the standard deviation of the indeterminacy.

In a material that is essentially compressed when the pressure increases, the uncertainty δx of the position measurement of the electrons inside decreases, so the uncertainty δp of the electron momentum increases according to the uncertainty principle. However, no matter how low the temperature drops, the electrons must move at Heisenberg speed because of the temperature and contribute to the pressure. When the electrons are made up of"Heisenberg speed"When the resulting pressure overrides the thermal motion, the electrons enter a degenerate state and the material becomes a degenerate state.

The electron degeneracy pressure prevents the core from collapsing before the stellar mass exceeds the Chandrasekhar limit (solar mass), which is the pressure that prevents the white dwarf from collapsing. Stars with masses beyond this limit and no fuel for nuclear fusion will continue to collapse to form neutron stars or black holes because the degenerate pressure provided by the electrons is not enough to resist gravity.

I think it's a strong interaction. The landlord seems to mean to ask Pauli about the principle of incompatibility. This may be equivalent to asking why the wave function of fermions is antisymmetric.

To the best of my ability, remember the nature of this antisymmetry ** under the spatial rotation of the su(2) group. And this group is used to describe strong interactions. Therefore, Pauli incompatibility principle should be a special manifestation of strong interaction for fermions.

If the landlord wants further details, I'll ask my advanced quantum mechanics teacher.

Pauli himself did not deduce Pauli's principle of incompatibility from somewhere, but only took it out of thin air, saying that the motion of fermions can be correctly deduced according to this principle. But now that we start from the relevant theories of quantum field theory, we can prove that if we require the field to be unitary, then we must require that the wave function of the wave chromon be symmetric, and the wave function of the fermion is antisymmetric. The physical meaning of unitary is that the sum of the probabilities of all events is one.

Therefore, Pauli's principle of incompatibility has nothing to do with the four fundamental functions, and its logical status is higher than the four fundamental effects. It is a logical deduction based on the basic requirement of the probability and unity of all events.

Considering the problem of electron rejection mentioned by the landlord, Pauli's incompatibility principle says that electrons cannot be in the same state, but it does not say that two electrons cannot be in the same place. In fact, the electrons in the atoms are all in a roughly the same place, and there is no force other than that used by Coulombs for each other. If you want to put an electron somewhere in space, you won't be subjected to "Pauli incompatible repulsion".

If you want to change the quantum numbers of two electrons to be exactly the same, that is, to change two electrons in the same orbital to the same spin, then this is simply not possible (no matter what physical means are used, the opposite properties of the spins of the two electrons will not change in the slightest), not that there will be strong resistance in the process of change. Therefore, there is no such thing as "Pauli incompatible repulsion" as the landlord calls it.

Pauli's principle of incompatibility refers to the original.

Electrons in the sub cannot be held in the exact same state of motion.

In chemistry, when atoms form molecules, stable covalent bonds are formed, and other electrons are separated.

This is a powerful method for quantum mechanics to explain the structure of molecules.

For example, a hydrogen molecule composed of two hydrogen atoms is very stable. The third atom cannot enter. Pauli incompatibility is a fundamental theorem of quantum science.

Found an explanation for degenerate substances:

Degenerate matter is a high-density state of matter. The pressure of a degenerate substance is mainly based on Pauli's incompatibility principle, which is called degenerate pressure. Since Pauli's principle of incompatibility prohibits different constituent particles from occupying the same quantum state, reducing the volume forces the particles into a high-energy state, resulting in a huge degeneracy pressure.

Depending on the composition of the particles, they are called electron degeneracy pressure, neutron degeneracy pressure, and so on.

Degenerate matter includes electron degenerate states, neutron degenerate states, metallic hydrogen, exotic matter, etc.

Please also refer to it.

The information in a black hole is completely unknown to the outside world, and the failure you are talking about is just a scientific inference. Moreover, the environment of black holes is only a special case in the universe. Most theories fail in an environment where time and space do not exist.

So you can't speculate on the principle of failure in a black hole.

All principles fail in black holes, so any inference is to put p, which is not part of the universe.

As long as the fermions satisfy the Pauli incompatibility principle, there is a degenerate pressure, but in reality, when the scale reaches the level and the neutron degeneracy pressure needs to be considered, the electrons have already been already"Press"The nucleus is neutralized with the protons, so there are usually no phenomena to consider it.

To put it simply, there are some particles (such as electrons, neutrons, protons, etc.) that are exclusive, they cannot occupy the same position in space, just like a group of naughty children, you want them to lean together, they will always push and push, to drive the children next to them far away, the closer they want to go, the greater the force to use, the mutual repulsion between this kind of particles, it is called degeneracy pressure.

Degenerate pressure is essentially a repulsive force that opposes gravity and is a manifestation of the anti-gravitational field.

First, the concept is different.

1. Hunt's principle: When electrons are distributed to atomic orbitals with reduced energy, they preferentially occupy different orbitals in the same way of spin, because the total energy of atoms in this arrangement is the lowest. So in orbitals of equal energy, the electrons spin parallel to each other as much as possible.

2. Pauli's principle: In a system composed of fermions, there cannot be two or more particles in exactly the same state. There cannot be two or more electrons with exactly the same four quantum numbers, or a maximum of two electrons can be accommodated in an atomic orbital determined by the orbital quantum numbers m,l,n, and the spin directions of these two electrons must be opposite.

Second, the proposer is different.

1. Hunt's Principle: Proposed by the German Friedrich Hunt.

2. Pauli's Principle: Proposed by Wolfgang Pauli.

3. Scope of application.

1. Hunt's principle: Hunt's rule only applies to the case of LS coupling. There are a few exceptions due to configuration interactions or deviations from LS coupling.

2. Pauli's principle: valid for all fermions (bosons), such as determining the atomic state of electrons in the same family, the mystery of helium atomic energy levels and Fermi-Dirac statistics.

It is not a collapse, but it should be called a "dense state" of matter.

Everyone who studies physics knows that in fact, the atom is very empty, the nucleus only occupies a small space, and most of the other space is occupied by the electron cloud, and the electrons are relaxed outside the nucleus.

And an important principle of particles involved here is the well-known "incompatibility principle". The principle of incompatibility states that no fermions can be in the same quantum state as other fermions.

We know that various elements will have a regular hierarchical structure with the increase of the number of electrons outside the nucleus, and there will be no situation where all the electrons outside the nucleus are all piled up, which is determined by the principle of quantum incompatibility. The quantum states of the individual electron orbitals are different, and the two electrons in the innermost shell, although they are in the same orbital, have opposite spins.

When a strong external force compresses an atom, the electron cloud begins to contract (electron wave function compression) and the electrons begin to resist this compression. When the electrons are compressed one after the other, their quantum wave wavelength is very short, and the kinetic energy is very large, and at this speed there is a huge support force for the surrounding collisions, which is the "electron degeneracy pressure" you see in the book.

The force of neutron degenerate compression is greater because neutrons are much heavier than protons.

No. It is a kind of effect that prevents collapse produced by the Pauli incompatibility principle.

There is another way to say it, and that is pancakes .