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  2. Pauli exclusion principle - Wikipedia

    en.wikipedia.org/wiki/Pauli_exclusion_principle

    In quantum mechanics, the Pauli exclusion principle states that two or more identical particles with half-integer spins (i.e. fermions) cannot simultaneously occupy the same quantum state within a system that obeys the laws of quantum mechanics. This principle was formulated by Austrian physicist Wolfgang Pauli in 1925 for electrons, and later ...

  3. Exchange interaction - Wikipedia

    en.wikipedia.org/wiki/Exchange_interaction

    Exchange interaction is the main physical effect responsible for ferromagnetism, and has no classical analogue. For bosons, the exchange symmetry makes them bunch together, and the exchange interaction takes the form of an effective attraction that causes identical particles to be found closer together, as in Bose–Einstein condensation.

  4. Pauli matrices - Wikipedia

    en.wikipedia.org/wiki/Pauli_matrices

    Pauli matrices. Wolfgang Pauli (1900–1958), c. 1924. Pauli received the Nobel Prize in physics in 1945, nominated by Albert Einstein, for the Pauli exclusion principle. In mathematical physics and mathematics, the Pauli matrices are a set of three 2 × 2 complex matrices that are traceless, Hermitian, involutory and unitary.

  5. Wolfgang Pauli - Wikipedia

    en.wikipedia.org/wiki/Wolfgang_Pauli

    Wolfgang Pauli. His godfather was Ernst Mach. He is not to be confused with Wolfgang Paul, who called Pauli his "imaginary part", [5] a pun with the imaginary unit i. Wolfgang Ernst Pauli (/ ˈpɔːli /; [6] German: [ˈvɔlfɡaŋ ˈpaʊli]; 25 April 1900 – 15 December 1958) was an Austrian theoretical physicist and one of the pioneers of ...

  6. Introduction to quantum mechanics - Wikipedia

    en.wikipedia.org/wiki/Introduction_to_quantum...

    Pauli formulated his exclusion principle, stating, "There cannot exist an atom in such a quantum state that two electrons within [it] have the same set of quantum numbers." [39] A year later, Uhlenbeck and Goudsmit identified Pauli's new degree of freedom with the property called spin whose effects were observed in the Stern–Gerlach experiment.

  7. Old quantum theory - Wikipedia

    en.wikipedia.org/wiki/Old_quantum_theory

    Scientists. v. t. e. The old quantum theory is a collection of results from the years 1900–1925 [1] which predate modern quantum mechanics. The theory was never complete or self-consistent, but was instead a set of heuristic corrections to classical mechanics. [2] The theory has come to be understood as the semi-classical approximation [3] to ...

  8. Spin–statistics theorem - Wikipedia

    en.wikipedia.org/wiki/Spin–statistics_theorem

    This is the Pauli exclusion principle: two identical fermions cannot occupy the same state. This rule does not hold for bosons. In quantum field theory, a state or a wavefunction is described by field operators operating on some basic state called the vacuum. In order for the operators to project out the symmetric or antisymmetric component of ...

  9. Fermi–Dirac statistics - Wikipedia

    en.wikipedia.org/wiki/Fermi–Dirac_statistics

    Statistical mechanics. Fermi–Dirac statistics is a type of quantum statistics that applies to the physics of a system consisting of many non-interacting, identical particles that obey the Pauli exclusion principle. A result is the Fermi–Dirac distribution of particles over energy states. It is named after Enrico Fermi and Paul Dirac, each ...