The Pauli principle (the principle of prohibition) is one of the fundamental principles of quantum mechanics , according to which two or more identical fermions (particles with a half-integer spin) cannot simultaneously be in the same quantum state .
The principle was formulated for electrons by Wolfgang Pauli in 1925 while working on a quantum-mechanical interpretation of the anomalous Zeeman effect and was subsequently extended to all particles with half - integer spin . A complete generalized proof of the principle was made by him in the Pauli theorem (theorem on the connection of spin with statistics) in 1940 in the framework of quantum field theory [1] . It follows from this theorem that the wave function of a system of fermions is antisymmetric with respect to their permutations, the behavior of systems of such particles is described by the Fermi – Dirac statistics .
The Pauli principle can be formulated as follows: within a quantum system, in a given quantum state, there can only be one fermion, the state of another must differ by at least one quantum number .
In statistical physics, the Pauli principle is sometimes formulated in terms of fill numbers : in a system of identical particles described by an antisymmetric wave function, fill numbers can take only two values
There is no classical analogue of the Pauli principle [2] .
Content
Atom structure and Pauli principle
The Pauli principle helps explain various physical phenomena. A consequence of the principle is the presence of electron shells in the structure of an atom , which, in turn, implies a variety of chemical elements and their compounds. The number of electrons in an individual atom is equal to the number of protons . Since electrons are fermions, the Pauli principle forbids them to accept the same quantum states. As a result, all electrons cannot be in the same quantum state with the lowest energy (for an unexcited atom), but sequentially fill quantum states with the lowest total energy (one should not forget that the electrons are indistinguishable from each other, and therefore it cannot be said that which quantum state a particular electron is located).
An example is the unexcited lithium atom (Li), in which two electrons are located on the 1s orbital (the lowest in energy), and their own angular momenta differ, and the third electron cannot occupy the 1s orbital, since the prohibition will be violated Pauli. Therefore, the third electron occupies the 2s orbital (the next lowest energy orbital after 1s).
Notes
- ↑ W. Pauli The principle of prohibition, the Lorentz group, the reflection of space, time and charge // Niels Bohr and the development of physics. - M., IL, 1958. - c. 46-74
- ↑ Physics of the microworld. - M., Soviet Encyclopedia, 1980. - p. 304
Literature
- Pauli V. “On the Relationship between the Filling of Electron Groups in an Atom and the Complex Structure of Spectra” (Received January 16, 1925) in the book Wolfgang Pauli Transactions in Quantum Theory: Quantum Theory. General principles of wave mechanics. Articles 1920-1928. ”M .: Nauka, 1975. pp. 645-660
- Pauli W. Uber den Zusammenhang des Abschlusses der Elektronengruppen in Atom mit der Komplexstruktur der Spektren, - Z. Phys., 1925, 31, 765-783.
- Pauli V. General principles of wave mechanics. - M.-L. : GITTL, 1947.
- Davydov A.S. Quantum mechanics. - Science, 1973. - S. 334.
See also
- Hund rule
- Klechkovsky's rule
- Wave function
- Pauli's theorem