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In physics, an observable is a physical property or physical quantity that can be measured. In classical mechanics, an observable is a real-valued "function" on the set of all possible system states, e.g., position and momentum. In quantum mechanics, an observable is described by a linear operator. For example, these operators might represent submitting the system to various electromagnetic fields and eventually reading a value.

Quantum mechanicsQuantum mechanicsQuantum mechanics, also known as quantum physics, is the fundamental physical theory that describes the behavior of matter and of light; the behaviors it models typically occur at and below the scale of atoms, and have often been described as counterintuitive. Its concepts and methods have been applied across many disciplines, including quantum chemistry, quantum biology, quantum field theory, quantum technology, and quantum information science.MomentumMomentumIn Newtonian mechanics, momentum (pl.: momenta or momentums; more specifically linear momentum or translational momentum) is the product of the mass and velocity of an object. It is a vector quantity, possessing a magnitude and a direction. If m is an object's mass and v is its velocity (also a vector quantity), then the object's momentum p (from Latin pellere "push, drive") is: 𝐩=m𝐯.Physical quantityPhysical quantityA physical quantity (or simply quantity) is a property of a material or system that can be quantified by measurement. A physical quantity can be expressed as a value, which is a pair of a numerical value and a unit of measurement. For example, the physical quantity mass, symbol m, can be quantified as m=nkg, where n is the numerical value and kg is the unit symbol (for kilogram). Vector quantities have, besides numerical value and unit, direction or orientation in space.Linear mapIn mathematics, and more specifically in linear algebra, a linear map, linear mapping, or linear operator is a particular kind of function between vector spaces, which respects the basic operations of vector addition and scalar multiplication. A standard example of a linear map is an m×n matrix, which takes vectors in n-dimensions into vectors in m-dimensions in a way that is compatible with addition of vectors, and multiplication of vectors by scalars.Physical propertyA physical property is any property of a physical system that is measurable. The changes in the physical properties of a system can be used to describe its changes between momentary states. A quantifiable physical property is called physical quantity. Measurable physical quantities are often referred to as observables.Classical mechanicsClassical mechanicsIn physics, classical mechanics is a theory that describes the effect of forces on the motion of macroscopic objects and bulk matter, without considering quantum effects, and often without incorporating relativistic effects either. It is used in describing the motion of objects such as projectiles and particles, parts of machinery, spacecraft, planets, stars, galaxies, deformable solids, fluids, macromolecules and other objects.MeasurementMeasurementMeasurement is the quantification of attributes of an object or event, which can be used to compare with other objects or events. In other words, measurement is a process of determining how large or small a physical quantity is as compared to a basic reference quantity of the same kind. The scope and application of measurement are dependent on the context and discipline.Electromagnetic fieldElectromagnetic fieldAn electromagnetic field (also EM field) is a physical field, varying in space and time, that represents the electric and magnetic influences generated by and acting upon electric charges. The field at any point in space and time can be regarded as a combination of an electric field and a magnetic field.Real numberReal numberNumber representing a continuous quantityReal numbers can be thought of as all points on a number line.In mathematics, a real number is a number that can be used to measure a continuous one-dimensionalquantity such as a length, duration or temperature. Here, continuous means that pairs of values can have arbitrarily small differences. Every real number can be almost uniquely represented by an infinite decimal expansion.PhysicsPhysicsScientific field of studyPhenomena and processes of physics’ various domains, clockwise from the upper left: a Newton's cradle (classical mechanics), entropic changes in a snowflake (thermodynamics), a Chladni figure (waves, oscillations & acoustics), the aurora borealis (geophysics & electromagnetism), an insect floating across a pond (fluid mechanics & biophysics), gravitational lensing (astrophysics, optics & relativity), the double-slit experiment (quantum mechanics), and a Feynman diagram of beta decay (nuclear physics & particle physics).Physics is the scientific study of matter, its fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force.Operator (physics)An operator is a function over a space of physical states onto another space of 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.Position (geometry)Position (geometry)In geometry, a position or position vector, also known as location vector or radius vector, is a Euclidean vector that represents a point P in space. Its length represents the distance in relation to an arbitrary reference origin O, and its direction represents the angular orientation with respect to given reference axes.

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