Self-adjointIn mathematics, and more specifically in abstract algebra, an element x of a *-algebra is self-adjoint if . A self-adjoint element is also Hermitian, though the reverse doesn't necessarily hold. A collection C of elements of a star-algebra is self-adjoint if it is closed under the involution operation. For example, if then since in a star-algebra, the set {x,y} is a self-adjoint set even though x and y need not be self-adjoint elements. In functional analysis, a linear operator on a Hilbert space is called self-adjoint if it is equal to its own adjoint A^∗.
Particle detectorIn experimental and applied particle physics, nuclear physics, and nuclear engineering, a particle detector, also known as a radiation detector, is a device used to detect, track, and/or identify ionizing particles, such as those produced by nuclear decay, cosmic radiation, or reactions in a particle accelerator. Detectors can measure the particle energy and other attributes such as momentum, spin, charge, particle type, in addition to merely registering the presence of the particle.
Operator (physics)In physics, an operator is a function over a space of physical states onto another space of physical states. The simplest example of the utility of operators is the study of symmetry (which makes the concept of a group useful in this context). Because of this, they are useful tools in classical mechanics. Operators are even more important in quantum mechanics, where they form an intrinsic part of the formulation of the theory.
CylinderA cylinder () has traditionally been a three-dimensional solid, one of the most basic of curvilinear geometric shapes. In elementary geometry, it is considered a prism with a circle as its base. A cylinder may also be defined as an infinite curvilinear surface in various modern branches of geometry and topology. The shift in the basic meaning—solid versus surface (as in ball and sphere)—has created some ambiguity with terminology. The two concepts may be distinguished by referring to solid cylinders and cylindrical surfaces.
ParticleIn the physical sciences, a particle (or corpuscule in older texts) is a small localized object which can be described by several physical or chemical properties, such as volume, density, or mass. They vary greatly in size or quantity, from subatomic particles like the electron, to microscopic particles like atoms and molecules, to macroscopic particles like powders and other granular materials. Particles can also be used to create scientific models of even larger objects depending on their density, such as humans moving in a crowd or celestial bodies in motion.
Hermitian adjointIn mathematics, specifically in operator theory, each linear operator on an inner product space defines a Hermitian adjoint (or adjoint) operator on that space according to the rule where is the inner product on the vector space. The adjoint may also be called the Hermitian conjugate or simply the Hermitian after Charles Hermite. It is often denoted by A† in fields like physics, especially when used in conjunction with bra–ket notation in quantum mechanics.
Electric displacement fieldIn physics, the electric displacement field (denoted by D) or electric induction is a vector field that appears in Maxwell's equations. It accounts for the electromagnetic effects of polarization and that of an electric field, combining the two in an auxiliary field. It plays a major role in topics such as the capacitance of a material, as well the response of dielectrics to electric field, and how shapes can change due to electric fields in piezoelectricity or flexoelectricity as well as the creation of voltages and charge transfer due to elastic strains.
Interpretations of quantum mechanicsAn interpretation of quantum mechanics is an attempt to explain how the mathematical theory of quantum mechanics might correspond to experienced reality. Although quantum mechanics has held up to rigorous and extremely precise tests in an extraordinarily broad range of experiments, there exist a number of contending schools of thought over their interpretation. These views on interpretation differ on such fundamental questions as whether quantum mechanics is deterministic or stochastic, local or non-local, which elements of quantum mechanics can be considered real, and what the nature of measurement is, among other matters.
Particle Data GroupThe Particle Data Group (PDG) is an international collaboration of particle physicists that compiles and reanalyzes published results related to the properties of particles and fundamental interactions. It also publishes reviews of theoretical results that are phenomenologically relevant, including those in related fields such as cosmology. The PDG currently publishes the Review of Particle Physics and its pocket version, the Particle Physics Booklet, which are printed biennially as books, and updated annually via the World Wide Web.
Scalar potentialIn mathematical physics, scalar potential, simply stated, describes the situation where the difference in the potential energies of an object in two different positions depends only on the positions, not upon the path taken by the object in traveling from one position to the other. It is a scalar field in three-space: a directionless value (scalar) that depends only on its location. A familiar example is potential energy due to gravity.
DimensionIn physics and mathematics, the dimension of a mathematical space (or object) is informally defined as the minimum number of coordinates needed to specify any point within it. Thus, a line has a dimension of one (1D) because only one coordinate is needed to specify a point on it - for example, the point at 5 on a number line. A surface, such as the boundary of a cylinder or sphere, has a dimension of two (2D) because two coordinates are needed to specify a point on it - for example, both a latitude and longitude are required to locate a point on the surface of a sphere.
Three-dimensional spaceIn geometry, a three-dimensional space (3D space, 3-space or, rarely, tri-dimensional space) is a mathematical space in which three values (coordinates) are required to determine the position of a point. Most commonly, it is the three-dimensional Euclidean space, the Euclidean n-space of dimension n=3 that models physical space. More general three-dimensional spaces are called 3-manifolds. Technically, a tuple of n numbers can be understood as the Cartesian coordinates of a location in a n-dimensional Euclidean space.
