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Quantum Superposition
Quantum superposition is a fundamental principle of quantum mechanics that states that linear combinations of solutions to the Schrödinger equation are also solutions of the Schrödinger equation. This follows from the fact that the Schrödinger equation is a linear differential equation in time and position. More precisely, the state of a system is given by a linear combination of all the eigenfunctions of the Schrödinger equation governing that system. An example is a qubit used in quantum information processing. A qubit state is most generally a superposition of the basis states , 0 \rangle and , 1 \rangle: : , \Psi \rangle = c_0, 0\rangle + c_1, 1\rangle, where , \Psi \rangle is the quantum state of the qubit, and , 0 \rangle, , 1 \rangle denote particular solutions to the Schrödinger equation in Dirac notation weighted by the two probability amplitudes c_0 and c_1 that both are complex numbers. Here , 0 \rangle corresponds to the classical 0 bit, and , 1 \r ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantum Superposition Of States And Decoherence
In physics, a quantum (: quanta) is the minimum amount of any physical entity (physical property) involved in an fundamental interaction, interaction. The fundamental notion that a property can be "quantized" is referred to as "the hypothesis of quantization (physics), quantization". This means that the Magnitude (mathematics), magnitude of the physical property can take on only Wiktionary:discrete, discrete values consisting of Multiple (mathematics), integer multiples of one quantum. For example, a photon is a single quantum of light of a specific frequency (or of any other form of electromagnetic radiation). Similarly, the energy of an electron bound within an atom is quantized and can exist only in certain discrete values. Atoms and matter in general are stable because electrons can exist only at discrete energy levels within an atom. Quantization is one of the foundations of the much broader physics of quantum mechanics. Quantization of energy and its influence on how energy ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Eigenvectors
In linear algebra, an eigenvector ( ) or characteristic vector is a Vector (mathematics and physics), vector that has its direction (geometry), direction unchanged (or reversed) by a given linear map, linear transformation. More precisely, an eigenvector \mathbf v of a linear transformation T is scalar multiplication, scaled by a constant factor \lambda when the linear transformation is applied to it: T\mathbf v=\lambda \mathbf v. The corresponding eigenvalue, characteristic value, or characteristic root is the multiplying factor \lambda (possibly a negative number, negative or complex number, complex number). Euclidean vector, Geometrically, vectors are multi-dimensional quantities with magnitude and direction, often pictured as arrows. A linear transformation Rotation (mathematics), rotates, Scaling (geometry), stretches, or Shear mapping, shears the vectors upon which it acts. A linear transformation's eigenvectors are those vectors that are only stretched or shrunk, with nei ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Piezoelectric
Piezoelectricity (, ) is the electric charge that accumulates in certain solid materials—such as crystals, certain ceramics, and biological matter such as bone, DNA, and various proteins—in response to applied stress (mechanics), mechanical stress. The piezoelectric effect results from the linear electromechanical interaction between the mechanical and electrical states in crystalline materials with no centrosymmetry, inversion symmetry. The piezoelectric effect is a reversible process (thermodynamics), reversible process: List of piezoelectric materials, materials exhibiting the piezoelectric effect also exhibit the reverse piezoelectric effect, the internal generation of a mechanical strain resulting from an applied electric field. For example, lead zirconate titanate crystals will generate measurable piezoelectricity when their static structure is Deformation (physics), deformed by about 0.1% of the original dimension. Conversely, those same crystals will change about 0.1 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
SQUID
A squid (: squid) is a mollusc with an elongated soft body, large eyes, eight cephalopod limb, arms, and two tentacles in the orders Myopsida, Oegopsida, and Bathyteuthida (though many other molluscs within the broader Neocoleoidea are also called ''squid'' despite not strictly fitting these criteria). Like all other cephalopods, squid have a distinct head, Symmetry (biology)#Bilateral symmetry, bilateral symmetry, and a mantle (mollusc), mantle. They are mainly soft-bodied, like octopuses, but have a small internal skeleton in the form of a rod-like gladius (cephalopod), gladius or pen, made of chitin. Squid diverged from other cephalopods during the Jurassic and occupy a similar Ecological niche, role to teleost fish as open-water predators of similar size and behaviour. They play an important role in the open-water food web. The two long tentacles are used to grab prey and the eight arms to hold and control it. The beak then cuts the food into suitable size chunks for swal ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Buckminsterfullerene
Buckminsterfullerene is a type of fullerene with the formula . It has a cage-like fused-ring structure ( truncated icosahedron) made of twenty hexagons and twelve pentagons, and resembles a football. Each of its 60 carbon atoms is bonded to its three neighbors. Buckminsterfullerene is a black solid that dissolves in hydrocarbon solvents to produce a violet solution. The substance was discovered in 1985 and has received intense study, although few real world applications have been found. Molecules of buckminsterfullerene (or of fullerenes in general) are commonly nicknamed buckyballs. Occurrence Buckminsterfullerene is the most common naturally occurring fullerene. Small quantities of it can be found in soot. It also exists in space. Neutral has been observed in planetary nebulae and several types of star. The ionised form, , has been identified in the interstellar medium, where it is the cause of several absorption features known as diffuse interstellar bands in the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Double Slit Experiment
In modern physics, the double-slit experiment demonstrates that light and matter can exhibit behavior of both classical Particle, particles and classical Wave, waves. This type of experiment was first performed by Thomas Young (scientist), Thomas Young in 1801, as a demonstration of the wave behavior of visible light. In 1927, Davisson–Germer experiment, Davisson and Germer and, independently, George Paget Thomson and his research student Alexander Reid demonstrated that electrons show the same behavior, which was later extended to atoms and molecules. Thomas Young's experiment with light was part of classical physics long before the development of quantum mechanics and the concept of wave–particle duality. He believed it demonstrated that the Christiaan Huygens, Christiaan Huygens' wave theory of light was correct, and his experiment is sometimes referred to as Young's interference experiment, Young's experiment or Young's slits. The experiment belongs to a general class of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Beryllium
Beryllium is a chemical element; it has Symbol (chemistry), symbol Be and atomic number 4. It is a steel-gray, hard, strong, lightweight and brittle alkaline earth metal. It is a divalent element that occurs naturally only in combination with other elements to form minerals. Gemstones high in beryllium include beryl (Aquamarine (gemstone), aquamarine, emerald, red beryl) and chrysoberyl. It is a Abundance of the chemical elements#Universe, relatively rare element in the universe, usually occurring as a product of the spallation of larger atomic nuclei that have collided with cosmic rays. Within the cores of stars, beryllium is depleted as it is fused into heavier elements. Beryllium constitutes about 0.0004 percent by mass of Earth's crust. The world's annual beryllium production of 220 tons is usually manufactured by extraction from the mineral beryl, a difficult process because beryllium bonds strongly to oxygen. In structural applications, the combination of high flexural ri ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mesoscopic
Mesoscopic physics is a subdiscipline of condensed matter physics that deals with materials of an intermediate size. These materials range in size between the nanoscale for a quantity of atoms (such as a molecule) and of materials measuring micrometres. The lower limit can also be defined as being the size of individual atoms. At the microscopic scale are bulk materials. Both mesoscopic and macroscopic objects contain many atoms. Whereas average properties derived from constituent materials describe macroscopic objects, as they usually obey the laws of classical mechanics, a mesoscopic object, by contrast, is affected by thermal fluctuations around the average, and its electronic behavior may require modeling at the level of quantum mechanics. A macroscopic electronic device, when scaled down to a meso-size, starts revealing quantum mechanical properties. For example, at the macroscopic level the conductance of a wire increases continuously with its diameter. However, at the me ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tensor Products
In mathematics, the tensor product V \otimes W of two vector spaces V and W (over the same field) is a vector space to which is associated a bilinear map V\times W \rightarrow V\otimes W that maps a pair (v,w),\ v\in V, w\in W to an element of V \otimes W denoted . An element of the form v \otimes w is called the tensor product of v and w. An element of V \otimes W is a tensor, and the tensor product of two vectors is sometimes called an ''elementary tensor'' or a ''decomposable tensor''. The elementary tensors span V \otimes W in the sense that every element of V \otimes W is a sum of elementary tensors. If bases are given for V and W, a basis of V \otimes W is formed by all tensor products of a basis element of V and a basis element of W. The tensor product of two vector spaces captures the properties of all bilinear maps in the sense that a bilinear map from V\times W into another vector space Z factors uniquely through a linear map V\otimes W\to Z (see the section below t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Spinor
In geometry and physics, spinors (pronounced "spinner" IPA ) are elements of a complex numbers, complex vector space that can be associated with Euclidean space. A spinor transforms linearly when the Euclidean space is subjected to a slight (infinitesimal transformation, infinitesimal) rotation, but unlike Euclidean vector, geometric vectors and tensors, a spinor transforms to its negative when the space rotates through 360° (see picture). It takes a rotation of 720° for a spinor to go back to its original state. This property characterizes spinors: spinors can be viewed as the "square roots" of vectors (although this is inaccurate and may be misleading; they are better viewed as "square roots" of Section (fiber bundle), sections of vector bundles – in the case of the exterior algebra bundle of the cotangent bundle, they thus become "square roots" of differential forms). It is also possible to associate a substantially similar notion of spinor to Minkowski space, in which cas ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Spin (physics)
Spin is an Intrinsic and extrinsic properties, intrinsic form of angular momentum carried by elementary particles, and thus by List of particles#Composite particles, composite particles such as hadrons, atomic nucleus, atomic nuclei, and atoms. Spin is quantized, and accurate models for the interaction with spin require relativistic quantum mechanics or quantum field theory. The existence of electron spin angular momentum is inferred from experiments, such as the Stern–Gerlach experiment, in which silver atoms were observed to possess two possible discrete angular momenta despite having no orbital angular momentum. The relativistic spin–statistics theorem connects electron spin quantization to the Pauli exclusion principle: observations of exclusion imply half-integer spin, and observations of half-integer spin imply exclusion. Spin is described mathematically as a vector for some particles such as photons, and as a spinor or bispinor for other particles such as electrons. Sp ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Electron
The electron (, or in nuclear reactions) is a subatomic particle with a negative one elementary charge, elementary electric charge. It is a fundamental particle that comprises the ordinary matter that makes up the universe, along with up quark, up and down quark, down quarks. Electrons are extremely lightweight particles that orbit the positively charged atomic nucleus, nucleus of atoms. Their negative charge is balanced by the positive charge of protons in the nucleus, giving atoms their overall electric charge#Charge neutrality, neutral charge. Ordinary matter is composed of atoms, each consisting of a positively charged nucleus surrounded by a number of orbiting electrons equal to the number of protons. The configuration and energy levels of these orbiting electrons determine the chemical properties of an atom. Electrons are bound to the nucleus to different degrees. The outermost or valence electron, valence electrons are the least tightly bound and are responsible for th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
