The operators corresponding to the spin along the x, y, and z direction, denoted S < sub > x </ sub >, S < sub > y </ sub >, and S < sub > z </ sub > respectively, can be represented using the Pauli matrices:

The Pauli matrices are a set of three 2 × 2 complex matrices which are Hermitian and unitary.

These matrices were used by, then named after, the Austrian-born physicist Wolfgang Pauli ( 1900 – 1958 ), in his 1925 study of spin in quantum mechanics.

Each Pauli matrix is Hermitian, and together with the identity I ( sometimes considered the zeroth Pauli matrix ), the Pauli matrices span the full vector space of 2x2 Hermitian matrices.

In the language of quantum mechanics, hermitian matrices are observables, so the Pauli matrices span the space of observables of the 2-dimensional complex Hilbert space.

* The determinants and traces of the Pauli matrices are:

* Together with the identity matrix I ( which is sometimes written as σ < sub > 0 </ sub >), the Pauli matrices form an orthogonal basis, in the sense of Hilbert-Schmidt, for the real Hilbert space of 2 × 2 complex Hermitian matrices, or the complex Hilbert space of all 2 × 2 matrices.

Each of the ( hermitian ) Pauli matrices has two eigenvalues, + 1 and − 1.

Note that in this vector dotted with Pauli vector operation the Pauli matrices are treated in a scalar like fashion, commuting with the vector basis elements.

The Pauli matrices obey the following commutation and anticommutation relations:

It is an abstract version of the algebra generated by the gamma or Pauli matrices.

Spinors were first applied to mathematical physics by Wolfgang Pauli in 1927, when he introduced spin matrices.

More specifically, instead of representing spinors as complex-valued 2D column vectors as Pauli had done, they represented them as complex-valued 2 × 2 matrices in which only the elements of the left column are non-zero.

Wolfgang Pauli was convinced that the effect named after him was real.

In February 1950, when he was at Princeton University, the cyclotron burnt, and he asked himself if this mischief belonged to such a Pauli effect, named after him.

Shortly after the existence of quarks was first proposed in 1964, Oscar W. Greenberg introduced the notion of color charge to explain how quarks could coexist inside some hadrons in otherwise identical quantum states without violating the Pauli exclusion principle.

Toivonen's father, Pauli Toivonen, had won the event 20 years earlier after ten cars, including the first four to cross the finishing line, were disqualified due to having non-standard headlights.

When people were officially allowed to live in St. Pauli at the end of the 17th century the city government moved workhouses and ( pestilence ) hospitals out of the city to ' Hamburger Berg ,' which later was named after its church, ' St.

A devout Roman Catholic throughout his life, Curtis would repair to a convent church in the early hours of Sunday morning after finishing the Saturday night set at the Star Club, St. Pauli, near Hamburg.

* Johannes Pauli ( b. 1450 / 54 ; d. after 1530 ), Franciscan monk, Schwank poet, trailblazer for the comic, pointed short story ( Fazetie ) in Early Renaissance Germany ( 1499 preacher at the Oppenheim Franciscan convent ).

He was asked by the Polish Brethren to take up the position of a champion of conscientious objection against the Byelorussian Symon Budny and the Greek Unitarian Jacobus Palaeologus after Gregory Pauli of Brzeziny had become indisposed, and thereby gained some respect among the Poles.

St. Pauli, however, was relegated again after the 2002 – 03 season, this time to the Regionalliga Nord, the German third division.

Officials inaugurated the new town a year after on January 7, 1919 naming Fortunato Arban town mayor. Before the citizens of Pauli won back their township, Inocente Sumague donated a piece of land for the construction of a church in 1916.

Wolfgang Pauli declared Jordan " rehabilitated " to the authorities some time after the war, allowing him to regain academic employment after a two-year period and then recover his full status as a tenured professor in 1953.

Little was the St. Pauli Girl for 2000, the second of the Playmate national spokesmodels for the beer brand after Jaime Bergman.

Neutrinos are elementary particles first detected in the 1950s, long after their theoretical prediction by theorist Wolfgang Pauli.

Nevertheless, one has to keep in mind that electrons are fermions ruled by the Pauli exclusion principle and cannot be distinguished from the other electrons in the atom.

In the end, this was solved by the discovery of modern quantum mechanics and the Pauli Exclusion Principle.

Bohr was born in Copenhagen in 1922, and grew up surrounded by physicists such as Wolfgang Pauli and Werner Heisenberg, who were working with his father at the Institute for Theoretical Physics ( now the Niels Bohr Institute ) at the University of Copenhagen.

Baryons are strongly interacting fermions — that is, they experience the strong nuclear force and are described by Fermi − Dirac statistics, which apply to all particles obeying the Pauli exclusion principle.

Drude's classical model was augmented by Felix Bloch, Arnold Sommerfeld, and independently by Wolfgang Pauli, who used quantum mechanics to describe the motion of a quantum electron in a periodic lattice.

This theory used the neutrino postulated in 1930 by Wolfgang Pauli, but still undetected.

In particle physics, a fermion ( a name coined by Paul Dirac from the surname of Enrico Fermi ) is any particle characterized by Fermi – Dirac statistics and following the Pauli exclusion principle ; fermions include all quarks and leptons, as well as any composite particle made of an odd number of these, such as all baryons and many atoms and nuclei.

In the language of Heisenberg's matrix mechanics, the hydrogen atom was first solved by Wolfgang Pauli using a rotational symmetry in four dimension generated by the angular momentum

* History of Finland: A selection of events and documents by Pauli Kruhse

This was followed by an open letter to the pope ( Admonitio paterna Pauli III ) in 1544, in which Calvin admonished Paul III for depriving the reformers of any prospect of rapprochement.

Then, the electrons to be placed in the molecular orbitals are slotted in one by one, keeping in mind the Pauli exclusion principle and Hund's rule of maximum multiplicity ( only 2 electrons, having opposite spins, per orbital ; place as many unpaired electrons on one energy level as possible before starting to pair them ).

While paired electrons are required by the Pauli exclusion principle to have their intrinsic (' spin ') magnetic moments pointing in opposite directions, causing their magnetic fields to cancel out, an unpaired electron is free to align its magnetic moment in any direction.

Wolfgang Pauli was also fascinated by the appearance of certain numbers, including 137, in physics.

The neutrino was postulated first by Wolfgang Pauli in 1930 to explain how beta decay could conserve energy, momentum, and angular momentum ( spin ).

Neutron stars are very hot and are supported against further collapse by quantum degeneracy pressure due to the Pauli exclusion principle.

File: Pauli. jpg | Wolfgang Pauli ( 1900-1958 ): pioneers of quantum physics, received the Nobel Prize in Physics in 1945 ( nominated by Albert Einstein ), formulated the Pauli exclusion principle involving spin theory ( underpinning the structure of matter and the whole of chemistry ), published the Pauli – Villars regularization, formulated the Pauli equation, coined the phrase ' not even wrong '

The principle was formulated by Austrian physicist Wolfgang Pauli in 1925.

Integer spin particles, bosons, are not subject to the Pauli exclusion principle: any number of identical bosons can occupy the same quantum state, as with, for instance, photons produced by a laser and Bose – Einstein condensate.