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Stronger Uncertainty Relations
Heisenberg's uncertainty relation is one of the fundamental results in quantum mechanics. Later Robertson proved the uncertainty relation for two general non-commuting observables, which was strengthened by Schrödinger. However, the conventional uncertainty relation like the Robertson-Schrödinger relation cannot give a non-trivial bound for the product of variances of two incompatible observables because the lower bound in the uncertainty inequalities can be null and hence trivial even for observables that are incompatible on the state of the system. The Heisenberg–Robertson–Schrödinger uncertainty relation was proved at the dawn of quantum formalism and is ever-present in the teaching and research on quantum mechanics. After about 85 years of existence of the uncertainty relation this problem was solved recently by Lorenzo Maccone and Arun K. Pati. The standard uncertainty relations are expressed in terms of the product of variances of the measurement results of the obser ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Uncertainty Relation
In quantum mechanics, the uncertainty principle (also known as Heisenberg's uncertainty principle) is any of a variety of mathematical inequalities asserting a fundamental limit to the accuracy with which the values for certain pairs of physical quantities of a particle, such as position, ''x'', and momentum, ''p'', can be predicted from initial conditions. Such variable pairs are known as complementary variables or canonically conjugate variables; and, depending on interpretation, the uncertainty principle limits to what extent such conjugate properties maintain their approximate meaning, as the mathematical framework of quantum physics does not support the notion of simultaneously well-defined conjugate properties expressed by a single value. The uncertainty principle implies that it is in general not possible to predict the value of a quantity with arbitrary certainty, even if all initial conditions are specified. Introduced first in 1927 by the German physicist Werner Hei ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Observables
In physics, an observable is a physical quantity that can be measured. Examples include position and momentum. In systems governed by classical mechanics, it is a real-valued "function" on the set of all possible system states. In quantum physics, it is an operator, or gauge, where the property of the quantum state can be determined by some sequence of operations. For example, these operations might involve submitting the system to various electromagnetic fields and eventually reading a value. Physically meaningful observables must also satisfy transformation laws that relate observations performed by different observers in different frames of reference. These transformation laws are automorphisms of the state space, that is bijective transformations that preserve certain mathematical properties of the space in question. Quantum mechanics In quantum physics, observables manifest as linear operators on a Hilbert space representing the state space of quantum states. The e ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Arun K
Arun may refer to: People * Arun (given name), including a list of people with that name * Ila Arun, Indian actress * Priya Arun (born 1967), Indian actress * Bharat Arun (born 1962), Indian Test cricketer Places * Arun, Badakhshan, Afghanistan * Arun (England), a region of southeasthern England ** Arun District, West Sussex, England * Arun Banner, an administrative division (banner) of Inner Mongolia, China * Arun, Sumatra, a vassal state, now in Indonesia * Arun gas field, Sumatra, Indonesia * Aran va Bidgol ('Aran and Bidgol'), Isfahan Province, Iran **Aran va Bidgol County * Arun rural municipality, Nepal * Wat Arun, a temple in Bangkok, Thailand Rivers and canals * Arun River, China–Nepal * River Arun, in West Sussex, England * Wey and Arun Canal, in the south east of England Other uses * Aruṇa, a god in Hinduism * ''Arun''-class lifeboat * , two ships of the Royal Navy See also * * * Aaron (other) * Arran (other) * Aruna (other) * Arru ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantum Mechanics
Quantum mechanics is a fundamental theory in physics that provides a description of the physical properties of nature at the scale of atoms and subatomic particles. It is the foundation of all quantum physics including quantum chemistry, quantum field theory, quantum technology, and quantum information science. Classical physics, the collection of theories that existed before the advent of quantum mechanics, describes many aspects of nature at an ordinary (macroscopic) scale, but is not sufficient for describing them at small (atomic and subatomic) scales. Most theories in classical physics can be derived from quantum mechanics as an approximation valid at large (macroscopic) scale. Quantum mechanics differs from classical physics in that energy, momentum, angular momentum, and other quantities of a bound system are restricted to discrete values ( quantization); objects have characteristics of both particles and waves (wave–particle duality); and there are limits to ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
