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Werner Heisenberg
Werner Karl Heisenberg (; ; 5 December 1901 – 1 February 1976) was a German theoretical physicist, one of the main pioneers of the theory of quantum mechanics and a principal scientist in the German nuclear program during World War II. He published his Umdeutung paper, ''Umdeutung'' paper in 1925, a major reinterpretation of old quantum theory. In the subsequent series of papers with Max Born and Pascual Jordan, during the same year, his matrix mechanics, matrix formulation of quantum mechanics was substantially elaborated. He is known for the uncertainty principle, which he published in 1927. Heisenberg was awarded the 1932 Nobel Prize in Physics "for the creation of quantum mechanics". Heisenberg also made contributions to the theories of the Fluid dynamics, hydrodynamics of turbulent flows, the atomic nucleus, ferromagnetism, cosmic rays, and subatomic particles. He introduced the concept of a wave function collapse. He was also instrumental in planning the first West Germa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Würzburg
Würzburg (; Main-Franconian: ) is, after Nuremberg and Fürth, the Franconia#Towns and cities, third-largest city in Franconia located in the north of Bavaria. Würzburg is the administrative seat of the Regierungsbezirk Lower Franconia. It spans the banks of the Main (river), Main river. Würzburg is situated approximately 110 km west-northwest of Nuremberg and 120 km east-southeast of Frankfurt, Frankfurt am Main. The population as of 2019 is approximately 130,000 residents. Würzburg is famous for its partly rebuilt and reconstructed old town and its Würzburger Residenz, a palace that is a List of World Heritage Sites in Germany, UNESCO World Heritage Site. The regional dialect is East Franconian German. History Early and medieval history A Bronze Age Europe, Bronze Age (Urnfield culture) refuge castle, the Celtic Segodunum, and later a Roman Empire, Roman fort, stood on the hill known as the Leistenberg, the site of the present Fortress Marienberg. The ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Euler–Heisenberg Lagrangian
In physics, the Euler–Heisenberg Lagrangian describes the non-linear dynamics of electromagnetic fields in vacuum and is consequently an example of nonlinear electrodynamics. It was first obtained by Werner Heisenberg and Hans Heinrich Euler in 1936. By treating the vacuum as a medium, it predicts rates of quantum electrodynamics (QED) light interaction processes. Physics It takes into account vacuum polarization to one loop, and is valid for electromagnetic fields that change slowly compared to the inverse electron mass, :\mathcal =-\mathcal -\frac\int_^\exp\left(-m^s\right)\left es)^\frac\mathcal-\frac(es)^\mathcal - 1\rightfrac. Here is the electron mass, the electron charge, \mathcal=\frac\left(\mathbf^2 - \mathbf^2\right), and \mathcal=\mathbf\cdot\mathbf. In the weak field limit, this becomes :\mathcal = \frac\left(\mathbf^-\mathbf^\right)+\frac\left left(\mathbf^2 - \mathbf^2\right)^ + 7 \left(\mathbf\cdot\mathbf\right)^\right It describes photon–photon scatte ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
S-matrix
In physics, the ''S''-matrix or scattering matrix is a Matrix (mathematics), matrix that relates the initial state and the final state of a physical system undergoing a scattering, scattering process. It is used in quantum mechanics, scattering theory and quantum field theory (QFT). More formally, in the context of QFT, the ''S''-matrix is defined as the unitary matrix connecting sets of asymptotically free particle states (the ''in-states'' and the ''out-states'') in the Hilbert space of physical states: a multi-particle state is said to be ''free'' (or non-interacting) if it Representation theory of the Lorentz group, transforms under Lorentz transformations as a tensor product, or ''direct product'' in physics parlance, of ''one-particle states'' as prescribed by equation below. ''Asymptotically free'' then means that the state has this appearance in either the distant past or the distant future. While the ''S''-matrix may be defined for any background (spacetime) that is a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Resonance (chemistry)
In chemistry, resonance, also called mesomerism, is a way of describing Chemical bond, bonding in certain molecules or polyatomic ions by the combination of several contributing structures (or ''forms'', also variously known as ''resonance structures'' or ''canonical structures'') into a resonance hybrid (or ''hybrid structure'') in valence bond theory. It has particular value for analyzing delocalized electrons where the bonding cannot be expressed by one single Lewis structure. The resonance hybrid is the accurate structure for a molecule or ion; it is an average of the theoretical (or hypothetical) contributing structures. Overview Under the framework of valence bond theory, resonance is an extension of the idea that the bonding in a chemical species can be described by a Lewis structure. For many chemical species, a single Lewis structure, consisting of atoms obeying the octet rule, possibly bearing formal charges, and connected by bonds of positive integer order, is suffi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Discovery Of The Neutron
The discovery of the neutron and its properties was central to the extraordinary developments in atomic physics in the first half of the 20th century. Early in the century, Ernest Rutherford developed a crude Rutherford model, model of the atom, based on the Geiger–Marsden experiment, gold foil experiment of Hans Geiger and Ernest Marsden. In this model, atoms had their mass and Electric charge, positive electric charge concentrated in a very small atomic nucleus, nucleus. By 1920, isotopes of chemical elements had been discovered, the atomic masses had been determined to be (approximately) Multiple (mathematics), integer multiples of the mass of the hydrogen atom, and the atomic number had been identified as the charge on the nucleus.Byrne, J. ''Neutrons, Nuclei, and Matter'', Dover Publications, Mineola, New York, 2011, Throughout the 1920s, the nucleus was viewed as composed of combinations of protons and electrons, the two elementary particles known at the time, but that mo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantum Spacetime
In mathematical physics, the concept of quantum spacetime is a generalization of the usual concept of spacetime in which some variables that ordinarily commute are assumed not to commute and form a different Lie algebra. The choice of that algebra varies from one theory to another. As a result of this change, some variables that are usually continuous may become discrete. Often only such discrete variables are called "quantized"; usage varies. The idea of quantum spacetime was proposed in the early days of quantum theory by Heisenberg and Ivanenko as a way to eliminate infinities from quantum field theory. The germ of the idea passed from Heisenberg to Rudolf Peierls, who noted that electrons in a magnetic field can be regarded as moving in a quantum spacetime, and to Robert Oppenheimer, who carried it to Hartland Snyder, who published the first concrete example. Snyder's Lie algebra was made simple by C. N. Yang in the same year. Overview Physical spacetime is a quantum spac ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantum Fluctuation
In quantum physics, a quantum fluctuation (also known as a vacuum state fluctuation or vacuum fluctuation) is the temporary random change in the amount of energy in a point in space, as prescribed by Werner Heisenberg's uncertainty principle. They are minute random fluctuations in the values of the fields which represent elementary particles, such as electric and magnetic fields which represent the electromagnetic force carried by photons, W and Z fields which carry the weak force, and gluon fields which carry the strong force. The uncertainty principle states the uncertainty in energy and time can be related by \Delta E \, \Delta t \geq \tfrac\hbar~, where ≈ . This means that pairs of virtual particles with energy \Delta E and lifetime shorter than \Delta t are continually created and annihilated in ''empty'' space. Although the particles are not directly detectable, the cumulative effects of these particles are measurable. For example, without quantum fluctuations, th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantum Field Theory
In theoretical physics, quantum field theory (QFT) is a theoretical framework that combines Field theory (physics), field theory and the principle of relativity with ideas behind quantum mechanics. QFT is used in particle physics to construct physical models of subatomic particles and in condensed matter physics to construct models of quasiparticles. The current standard model of particle physics is based on QFT. History Quantum field theory emerged from the work of generations of theoretical physicists spanning much of the 20th century. Its development began in the 1920s with the description of interactions between light and electrons, culminating in the first quantum field theory—quantum electrodynamics. A major theoretical obstacle soon followed with the appearance and persistence of various infinities in perturbative calculations, a problem only resolved in the 1950s with the invention of the renormalization procedure. A second major barrier came with QFT's apparent inabili ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Optical Theorem
In physics, the optical theorem is a general law of wave scattering theory, which relates the zero-angle scattering amplitude to the total cross section of the scatterer. It is usually written in the form :\sigma=\frac~\mathrm\,f(0), where (0) is the scattering amplitude with an angle of zero, that is the amplitude of the wave scattered to the center of a distant screen and is the wave vector in the incident direction. Because the optical theorem is derived using only conservation of energy, or in quantum mechanics from conservation of probability, the optical theorem is widely applicable and, in quantum mechanics, \sigma_\mathrm includes both elastic and inelastic scattering. The generalized optical theorem, first derived by Werner Heisenberg, follows from the unitary condition and is given by :f(\mathbf,\mathbf') -f^*(\mathbf',\mathbf)= \frac \int f(\mathbf,\mathbf'')f^*(\mathbf',\mathbf'')\,d\Omega'' where f(\mathbf,\mathbf') is the scattering amplitude that depends on the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Exchange Interaction
In chemistry and physics, the exchange interaction is a quantum mechanical constraint on the states of indistinguishable particles. While sometimes called an exchange force, or, in the case of fermions, Pauli repulsion, its consequences cannot always be predicted based on classical ideas of force. Both bosons and fermions can experience the exchange interaction. The wave function of identical particles, indistinguishable particles is subject to exchange symmetry: the wave function either changes sign (for fermions) or remains unchanged (for bosons) when two particles are exchanged. The exchange symmetry alters the Expectation value (quantum mechanics), expectation value of the distance between two indistinguishable particles when their wave functions overlap. For fermions the expectation value of the distance increases, and for bosons it decreases (compared to distinguishable particles). The exchange interaction arises from the combination of exchange symmetry and the Coulomb's l ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Matrix Mechanics
Matrix mechanics is a formulation of quantum mechanics created by Werner Heisenberg, Max Born, and Pascual Jordan in 1925. It was the first conceptually autonomous and logically consistent formulation of quantum mechanics. Its account of quantum jumps supplanted the Bohr model's electron orbits. It did so by interpreting the physical properties of particles as matrices that evolve in time. It is equivalent to the Schrödinger wave formulation of quantum mechanics, as manifest in Dirac's bra–ket notation. In some contrast to the wave formulation, it produces spectra of (mostly energy) operators by purely algebraic, ladder operator methods. Relying on these methods, Wolfgang Pauli derived the hydrogen atom spectrum in 1926, before the development of wave mechanics. Development of matrix mechanics In 1925, Werner Heisenberg, Max Born, and Pascual Jordan formulated the matrix mechanics representation of quantum mechanics. Epiphany at Helgoland In 1925 Werner Heisenberg w ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Isospin
In nuclear physics and particle physics, isospin (''I'') is a quantum number related to the up- and down quark content of the particle. Isospin is also known as isobaric spin or isotopic spin. Isospin symmetry is a subset of the flavour symmetry seen more broadly in the interactions of baryons and mesons. The name of the concept contains the term ''spin'' because its quantum mechanical description is mathematically similar to that of angular momentum (in particular, in the way it couples; for example, a proton–neutron pair can be coupled either in a state of total isospin 1 or in one of 0). But unlike angular momentum, it is a dimensionless quantity and is not actually any type of spin. Before the concept of quarks was introduced, particles that are affected equally by the strong force but had different charges (e.g. protons and neutrons) were considered different states of the same particle, but having isospin values related to the number of charge states. A close exami ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
