Pauli exclusion principle, also known as Pauli principle and exclusion principle, isMicroparticleOne of the basic laws of motion.It points out that:FermionIn the composed system, there cannot be two or more particles in the same state.stayatomFour are required to completely determine the state of an electron inQuantum numberTherefore, the Pauli exclusion principle in atoms is shown as: no two or more electrons can have exactly the same four quantum numbers, or in other words, the orbital quantum numbersm，l，nDefinitiveAtomic orbitalA maximum of two electrons can be accommodated on theSpin directionThe opposite must be true.This is the formation of electrons arranged outside the nucleusPeriodicityTo explainperiodic table of ele mentsOne of the guidelines of.
Extranuclear electron arrangementFollowing the Pauli exclusion principlePrinciple of minimum energyandHunt rule。The principle of the lowest energy is that on the premise of not violating the Pauli exclusion principle, the extranuclear electrons always occupy the lowest energy orbit first. Only when the lowest energy orbit is full, the electrons will enter the higher energy orbit in turn, that is, to make the system energy as low as possible.The Hunt rule is based on the equivalent orbit (the sameElectronic layer、Electronic sublayerThe electrons arranged on () will occupy different orbits as much as possible, andSpin directionSame.Later, quantum mechanics proved that this arrangement of electrons can minimize the energy, so the Hunt rule can be included in the energy minimum principle as a supplement to the energy minimum principle[1]。
Pauli exclusion principle isspinbySemiintegerParticles of（Fermion）This principle is called Pauli principle for short.It can be expressed as that there can be no two or more particles in the same Fermion system at the same timeSingle particle state。The spin of the electron is 1/2, so it follows the Pauli principle.In 1925 byWolfgang PauliTo illustrate the periodic law of chemical elements, Pauli initially proposed that no two electrons in an atom can have identical quantum states when summarizing the atomic structure.atomThe state of the electrons in thePrincipal quantum numbern、Angular quantum numberl、Magnetic quantum numbermas well asSpin quantum numbermsTherefore, the Pauli principle can be expressed as that it is impossible for two or more electrons in an atom to have exactly the same four quantum numbersn、l、m、ms。According to Pauli principle, the periodic law of chemical elements can be well explained.Pauli principle is an important principle followed by all fermions. In all systems containing electronsValence bond theoryMedium, in solid metalsemiconductorandinsulatorAll of them play an important role in the theory.Later, it was known that Pauli's principle was also applicable to others such asproton、neutronWait for Fermion.Pauli principle is the basis for understanding many natural phenomena.
The wave function of a quantum system consisting of two fermions is completely anti symmetric.[2]
history
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development history
1913Bohr(N. Bohr) published the landmark hydrogen atom theory, which integratesrutherford(E. Rutherford) Nucleated atom model andEinstein(A. Einstein) quantum theory, which predicts the existence of stable states in the atom and perfectly explains the hydrogen atombalmer (J. Balmer) line system, giving the J. Rydberg constant which is completely consistent with the experiment.[4]
1916sommerfeld (A. Sommerfeld) extended the Bohr circular orbit of the hydrogen atom to the elliptical orbit, and further considered the relativistic effect, gavedirac (P. A. M. Dirac) equation to calculate the energy level formula of the identical hydrogen atom.[4]
In 1922, Bohr upgraded the hydrogen atom theory, pointed out that the periodic change of element properties is the result of the arrangement of electrons in the atom according to a certain shell, and made a physical explanation of the periodic law of elements. According to the atomic spectrum data, Bohr gave the maximum number of electrons that can be accommodated in the (main) shell where the main quantum number n is located as.[4]
In 1924, E. Stoner used the marking method of element characteristic X-ray quantum numbers to rearrange Bohr's shell filled with electrons.[4]
On the basis of Stoner's work, W. Pauli discovered the Pauli incompatibility principle in 1925, introduced the fourth quantum number to express the intrinsic properties of the electron on the basis of Stoner's three quantum numbers, and predicted that the fourth quantum number had only two values.We know that the Pauli exclusion principle gives the fourth quantum number of the electronUlenbeck(G. Uhlenbeck) and S. Goudsmit give the meaning of spin.[4]
As soon as Pauli exclusion principle was discovered, it was quickly applied to the establishment of quantum mechanics.1926Heisenberg (W. Heisenberg) constructed the antisymmetric wave function of two electrons of helium atom according to Pauli incompatibility, and solved the mystery of "normal helium" and "secondary helium" spectra of helium atom.In the same year, Dirac also constructed the antisymmetric wave function of multiple electrons, and he further discovered the distribution of identical particles satisfying the Pauli exclusion principle at different energy levels and temperatures, several months earlierFermi(E. Fermi) also found this distribution function independently.[4]
Pauli himself
Pauli was admitted in 1918University of Munichattend school,Arnold Sommerfeld He is the guiding professor of his doctoral thesis. They often discuss the problems about atomic structure, especially the integer sequence discovered by Rydberg earlier. Each integer is the maximum number of electrons that can be accommodated in the corresponding electronic layer, which seems to be of special significance.In 1921, Pauli received his doctor's degree. In his doctoral dissertation, he applied the Bohr Sommerfeld model to analyze the hydrogen molecular ion Htwo+Question.After graduation, Pauli appliedUniversity of GottingenbecomeMax Born He is an assistant in the application of astronomical perturbation theory to atomic physics.In 1922, Bohr invited Pauli toUniversity of CopenhagenBohr Institute.There, Pauli tried to explain the experimental results of the abnormal Zeeman effect in the field of atomic spectroscopy, that is, in the weak external magnetic fieldalkali metalThe exhibit shows a double line spectrum rather than a normal triple line spectrum.Pauli could not find a satisfactory solution, so he could only extend his research and analysis to the situation of strong external magnetic field, that isPaschen Buck effect(Paschen Backer effect), because the strong external magnetic field can decouple the spin and atomic orbit, the problem is simplified. This research is very helpful for discovering the incompatibility principle in the future.
The next year, Pauli was hired asHamburger University Lecturer in physics, he began to study the physical mechanism of forming a closed shell, and thought that this problem was related to the multiline structure, so he focused more on the researchalkali metalDouble line structure of.According to the mainstream view advocated by Bohr at that time, because of the limited angular momentum of the atomic nucleus, there will be a double wire structure.Pauli disagreed with this argument. In 1924, he published a paper indicating that the double wire structure of alkali metals is due to a quantum property possessed by electrons, which is a "double value property" that cannot be described by classical mechanical theory.For this reason, he proposed to set a new double value quantum number, and only one of the two values can be selected as the quantum number.Later, Samuel Goudsmit and George Ulenbeck confirmed that this property is the spin of electrons.
Electronic arrangement
From Edmund Stoner's 1924 paper, Pauli found an important clue to explain the electronic arrangement, and Stoner proposed to divide the electronic layer into severalElectronic sublayer, according toAngular quantum numberEach electron sublayer can accommodate up to 2 electrons.Pauli keenly observed that in the closed shell, each electron sublayer has two electrons, because each electron can only occupy onequantum state；The angular quantum number of the electron and the self angular quantum number (1/2) jointly contribute toTotal angular quantum number；The magnetic quantum number of the electron and the self binding magnetic quantum number (+1/2 or - 1/2) together contribute to the total magnetic quantum number.In 1925, Pauli published a paper formally proposing the Pauli exclusion principle: each electron in the closed shell has its unique electronic state, which is defined by four quantum numbers.
In 1940, Pauli's theory deduced the relationship between the spin and statistical properties of particles, thus proving that the principle of incompatibility is the inevitable consequence of relativistic quantum mechanics.
Paul EhrenfestIn 1931, it was pointed out that due to the Pauli exclusion principle, the bound electrons inside the atom will not all fall into the atomic orbital with the lowest energy, and they must occupy the atomic orbital with higher and higher energy in order.Therefore, the atom will have a certain volume, and the material will be so large.In 1967,Freeman DysonAnd Andrew Lenard, who calculated the balance between attraction (electron and nucleon) and repulsion (electron and electron, nucleon and nucleon), and deduced an important result: if the principle of incompatibility is not valid, ordinary matter willCollapse, occupying a very small volume.[3]
In 1964,quarkShortly after its existence was proposed, Oscar Greenberg introducedChromophoraTo explain how the three quarks can be formed togetherbaryon, which is in the same state in other aspects but still meets the Pauli exclusion principle.This concept later proved useful and becameQuark model(quark model).In the 1970s,Quantum chromodynamicsStart to develop and formParticle physicsIt is an important component of the standard model.[1]
Establishment of principle
As early as 1921, Pauli was deeply attracted by the development of quantum theory. When he was a graduate studentAnomalous Zeeman effectHas a strong interest.so-calledZeeman effectThat is, under the action of a strong magnetic field, the energy levels of atoms, molecules and crystals change, and the emitted spectral lines split.
Zeeman effect can be divided into two types: one exists when the spin magnetic moment of the electron is zero, which is calledNormal Zeeman effect；The other is the case when the spin magnetic moment of the electron is ± 1/2, which is called the abnormal Zeeman effect. The abnormal Zeeman effect is the common phenomenon of atomic spectral line splitting. This name, contrary to the actual situation, reflects the historical limitations of human cognitive process.At the end of 1924, in order to correctly understand the abnormal Zeeman effect, Pauli carefully studied the dual structure of the alkali metal spectrum on the basis of analyzing a large number of atomic energy level data, introduced the concept of "dual value that cannot be described by the classics", and wrote a paper entitled "The complex structure of the electron group and spectrum in atoms".
Before 1925, only three quantum numbers were used to describe the electron. Pauli's "double value" actually means that the electron must have the fourth quantum number.Because Pauli felt that the formulation of physical thought in this paper was too abstract to make up his mind, he sent the article to Bohr, who immediately encouraged him to submit it to the Journal of Physics, which was published in early 1925.It was this article that proposed the Pauli exclusion principle, which provided a theoretical basis for explaining the periodicity of the chemical elements of D.1 Mendeleev, and also laid the foundation for his future Nobel Prize.[3]
Principle explanation
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Pauli exclusion principle
If the sign of the wave function value changes after any two particles are exchanged, then thiswave functionIt is completely antisymmetric.This means that two fermions can never occupy the same place in the same systemquantum state。Since all quantum particles are indistinguishable, if the quantum states of two fermions are identical, the value of the wave function should not change after they are exchanged.The solution of this paradox is that the value of the wave function is zero:
For example, in the above example, if the position of two particleswave functionIf they are consistent, their spin wave functions must be antisymmetric, that is, their spins must be opposite.
This principle shows that two electrons or two fermions of any other kind cannot occupy identical quantum states.Also known as Pauli exclusion principle.
Application of principle
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Pauli exclusion principle is a basic principle in modern physics, from which many results can be derived, such as the determination of atomic states of the same family of electrons, the mystery of energy levels of helium atoms and Fermi Dirac statistics.
Homologous electronic atomic state
Four quantum numbers are used for the state of electrons in atoms（n，l，m，ms）Description, wherenMajor quantum number,lIs the orbital angular momentum quantum number,M isOrbital magnetic quantum number,msIs the spin magnetic quantum number.The use of four quantum numbers is a common marking method in modern times, rather than the marking adopted by Pauli at that time.Principal quantum numbernAnd orbital angular momentum quantum numberslThe same electrons are called homologous electrons. The atomic states of homologous electrons need to take into account the limits of Pauli exclusion principle.The Pauli exclusion principle is expressed as that it is impossible for two or more electrons in an atom to have exactly the same four quantum numbers（n，l，m，ms）。
The Mystery of Helium Atomic Energy Level
With the help of Pauli exclusion principle, Heisenberg proposed that the wave function of multi electron atoms is antisymmetric, which was the first to uncover the mystery of the energy level of helium atoms.
Fermi Dirac statistics
In 1926, E. Fermi found that the symmetric wave function called Fermi Dirac distribution followed by the monatomic ideal gas following the Pauli exclusion principle was the same as the function of other potential energy terms in 1926, but Fermi did not give a specific derivation process.Fermi studied the quantization (degeneracy) problem of monatomic ideal gas at low temperature according to Fermi Dirac distribution function. Fermi gave the expression of average kinetic energy, pressure, entropy and specific heat of ideal gas (proportional to temperature), which solved the problem of free electrons in metal comparing heat contribution.
In the same year, Dirac constructed a multiparticle system satisfying Pauli's incompatibility theory in an article on quantum mechanics theoryAntisymmetric wave functionDirac also realized that the wave function satisfying Bose Einstein statistics is a multiparticle wave function that is symmetric.Dirac also independently derived the Fermi Dirac distribution function of identical particles satisfying the Pauli exclusion principle at different energy levels and temperatures. According to the Fermi Dirac distribution function, he also studied the energy and pressure of Fermi gas, pointed out that the specific heat of Fermi gas is proportional to the first power of temperature, and also developedPerturbation theoryThe expression of B coefficient in Einstein's stimulated radiation theory is given.[4]
