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Pauli exclusion principle

Pauli exclusion principle
A more rigorous statement is that the total wave function for two identical fermions is anti-symmetric with respect to exchange of the particles. This means that the wave function changes its sign if the space and spin co-ordinates of any two particles are interchanged. 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. Overview[edit] "Half-integer spin" means that the intrinsic angular momentum value of fermions is (reduced Planck's constant) times a half-integer (1/2, 3/2, 5/2, etc.). History[edit] In the early 20th century it became evident that atoms and molecules with even numbers of electrons are more chemically stable than those with odd numbers of electrons. Pauli looked for an explanation for these numbers, which were at first only empirical. Connection to quantum state symmetry[edit] and the other in state


Boson In quantum mechanics, a boson (/ˈboʊsɒn/,[1] /ˈboʊzɒn/[2]) is a particle that follows Bose–Einstein statistics. Bosons make up one of the two classes of particles, the other being fermions.[3] The name boson was coined by Paul Dirac[4] to commemorate the contribution of the Indian physicist Satyendra Nath Bose[5][6] in developing, with Einstein, Bose–Einstein statistics—which theorizes the characteristics of elementary particles.[7] Examples of bosons include fundamental particles such as photons, gluons, and W and Z bosons (the four force-carrying gauge bosons of the Standard Model), the recently discovered Higgs boson, and the hypothetical graviton of quantum gravity; composite particles (e.g. mesons and stable nuclei of even mass number such as deuterium (with one proton and one neutron, mass number = 2), helium-4, or lead-208[Note 1]); and some quasiparticles (e.g. Cooper pairs, plasmons, and phonons).[8]:130 Types[edit]

Quantum hydrodynamics Quantum hydrodynamics (QHD) is most generally the study of hydrodynamic systems which demonstrate behavior implicit in quantum subsystems (usually quantum tunnelling). They arise in semiclassical mechanics in the study of semiconductor devices, in which case being derived from the Wigner–Boltzmann equation. In quantum chemistry they arise as solutions to chemical kinetic systems, in which case they are derived from the Schrödinger equation by way of Madelung equations. An important system of study in quantum hydrodynamics is that of superfluidity.

Uncertainty principle where ħ is the reduced Planck constant. The original heuristic argument that such a limit should exist was given by Heisenberg, after whom it is sometimes named the Heisenberg principle. This ascribes the uncertainty in the measurable quantities to the jolt-like disturbance triggered by the act of observation. Though widely repeated in textbooks, this physical argument is now known to be fundamentally misleading.[4][5] While the act of measurement does lead to uncertainty, the loss of precision is less than that predicted by Heisenberg's argument; the formal mathematical result remains valid, however. Since the uncertainty principle is such a basic result in quantum mechanics, typical experiments in quantum mechanics routinely observe aspects of it.

Fermion Antisymmetric wavefunction for a (fermionic) 2-particle state in an infinite square well potential. In particle physics, a fermion (a name coined by Paul Dirac[1] from the surname of Enrico Fermi) is any particle characterized by Fermi–Dirac statistics. These particles obey 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. Fermions differ from bosons, which obey Bose–Einstein statistics.

Quantum electrodynamics In particle physics, quantum electrodynamics (QED) is the relativistic quantum field theory of electrodynamics. In essence, it describes how light and matter interact and is the first theory where full agreement between quantum mechanics and special relativity is achieved. QED mathematically describes all phenomena involving electrically charged particles interacting by means of exchange of photons and represents the quantum counterpart of classical electromagnetism giving a complete account of matter and light interaction. History[edit] The first formulation of a quantum theory describing radiation and matter interaction is attributed to British scientist Paul Dirac, who (during the 1920s) was first able to compute the coefficient of spontaneous emission of an atom.[2] Difficulties with the theory increased through the end of 1940.

Zero-point energy Zero-point energy, also called quantum vacuum zero-point energy, is the lowest possible energy that a quantum mechanical physical system may have; it is the energy of its ground state. All quantum mechanical systems undergo fluctuations even in their ground state and have an associated zero-point energy, a consequence of their wave-like nature. The uncertainty principle requires every physical system to have a zero-point energy greater than the minimum of its classical potential well. This results in motion even at absolute zero.

Second quantization Second quantization is a powerful procedure used in quantum field theory for describing the many-particle systems by quantizing the fields using a basis that describes the number of particles occupying each state in a complete set of single-particle states. This differs from the first quantization, which uses the single-particle states as basis. Introduction[edit] The starting point of this formalism is the notion of indistinguishability of particles that bring us to use determinants of single-particle states as a basis of the Hilbert space of N-particles states[clarification needed]. Quantum theory can be formulated in terms of occupation numbers (number of particles occupying one determined energy state) of these single-particle states. The formalism was introduced in 1927 by Dirac.[1]

First quantization A first quantization of a physical system is a semi-classical treatment of quantum mechanics, in which particles or physical objects are treated using quantum wave functions but the surrounding environment (for example a potential well or a bulk electromagnetic field or gravitational field) is treated classically. First quantization is appropriate for studying a single quantum-mechanical system being controlled by a laboratory apparatus that is itself large enough that classical mechanics is applicable to most of the apparatus. Theoretical background[edit] The starting point is the notion of quantum states and the observables of the system under consideration.

Wave–particle duality Origin of theory[edit] The idea of duality originated in a debate over the nature of light and matter that dates back to the 17th century, when Christiaan Huygens and Isaac Newton proposed competing theories of light: light was thought either to consist of waves (Huygens) or of particles (Newton). Through the work of Max Planck, Albert Einstein, Louis de Broglie, Arthur Compton, Niels Bohr, and many others, current scientific theory holds that all particles also have a wave nature (and vice versa).[2] This phenomenon has been verified not only for elementary particles, but also for compound particles like atoms and even molecules. For macroscopic particles, because of their extremely short wavelengths, wave properties usually cannot be detected.[3]

Classical field theory A physical field can be thought of as the assignment of a physical quantity at each point of space and time. For example, in a weather forecast, the wind velocity during a day over a country is described by assigning a vector to each point in space. Each vector represents the direction of the movement of air at that point.

Quantum mechanics Solution to Schrödinger's equation for the hydrogen atom at different energy levels. The brighter areas represent a higher probability of finding an electron. Quantum mechanics gradually arose from Max Planck's solution in 1900 to the black-body radiation problem (reported 1859) and Albert Einstein's 1905 paper which offered a quantum-based theory to explain the photoelectric effect (reported 1887).

Wave function However, complex numbers are not necessarily used in all treatments. Louis de Broglie in his later years proposed a real-valued wave function connected to the complex wave function by a proportionality constant and developed the de Broglie–Bohm theory. The unit of measurement for ψ depends on the system. For one particle in three dimensions, its units are [length]−3/2.

Renormalization In quantum field theory, the statistical mechanics of fields, and the theory of self-similar geometric structures, renormalization is any of a collection of techniques used to treat infinities arising in calculated quantities. When describing space and time as a continuum, certain statistical and quantum mechanical constructions are ill defined. To define them, the continuum limit has to be taken carefully. Renormalization establishes a relationship between parameters in the theory when the parameters describing large distance scales differ from the parameters describing small distances.

Spin (physics) In quantum mechanics and particle physics, spin is an intrinsic form of angular momentum carried by elementary particles, composite particles (hadrons), and atomic nuclei.[1][2] Spin is a solely quantum-mechanical phenomenon; it does not have a counterpart in classical mechanics (despite the term spin being reminiscent of classical phenomena such as a planet spinning on its axis).[2] Spin is one of two types of angular momentum in quantum mechanics, the other being orbital angular momentum. Orbital angular momentum is the quantum-mechanical counterpart to the classical notion of angular momentum: it arises when a particle executes a rotating or twisting trajectory (such as when an electron orbits a nucleus).[3][4] The existence of spin angular momentum is inferred from experiments, such as the Stern–Gerlach experiment, in which particles are observed to possess angular momentum that cannot be accounted for by orbital angular momentum alone.[5] where h is the Planck constant.