Bernard Lippmann
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Bernard Lippmann
Bernard Abram Lippmann. (August 18, 1914 – February 12, 1988) was an American theoretical physicist. A former Professor of Physics at New York University, Lippmann is mainly known for the Lippmann-Schwinger equation, a widely used tool in non-relativistic scattering theory, which he formulated together with his doctoral supervisor Julian Schwinger Biography Bernard Lippmann was born in Brooklyn, New York City, in 1914. After initially attending the New York University Polytechnic School of Engineering, Polytechnic School of Brooklyn, where he attained a bachelor's degree in electrical engineering, he switched to physics and was admitted to the degree of Master of Science at the University of Michigan in 1935 Subsequently, Lippmann entered the industry, where he held various engineering roles until the entry of the United States into the World War II, Second World War when he joined Massachusetts Institute of Technology, MIT's Radiation Laboratory (MIT), Radiation Laboratory. Fro ...
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New York City, New York
New York, often called New York City or NYC, is the List of United States cities by population, most populous city in the United States. With a 2020 population of 8,804,190 distributed over , New York City is also the List of United States cities by population density, most densely populated major city in the United States, and is more than twice as populous as second-place Los Angeles. New York City lies at the southern tip of New York (state), New York State, and constitutes the geographical and demographic center of both the Northeast megalopolis and the New York metropolitan area, the largest metropolitan area in the world by urban area, urban landmass. With over 20.1 million people in its metropolitan statistical area and 23.5 million in its combined statistical area as of 2020, New York is one of the world's most populous Megacity, megacities, and over 58 million people live within of the city. New York City is a global city, global Culture of New ...
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Master Of Science
A Master of Science ( la, Magisterii Scientiae; abbreviated MS, M.S., MSc, M.Sc., SM, S.M., ScM or Sc.M.) is a master's degree in the field of science awarded by universities in many countries or a person holding such a degree. In contrast to the Master of Arts degree, the Master of Science degree is typically granted for studies in sciences, engineering and medicine and is usually for programs that are more focused on scientific and mathematical subjects; however, different universities have different conventions and may also offer the degree for fields typically considered within the humanities and social sciences. While it ultimately depends upon the specific program, earning a Master of Science degree typically includes writing a thesis. The Master of Science degree was first introduced at the University of Michigan in 1858. One of the first recipients of the degree was De Volson Wood, who was conferred a Master of Science degree at the University of Michigan in 1859. Al ...
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Cross Section (physics)
In physics, the cross section is a measure of the probability that a specific process will take place when some kind of radiant excitation (e.g. a particle beam, sound wave, light, or an X-ray) intersects a localized phenomenon (e.g. a particle or density fluctuation). For example, the Rutherford cross-section is a measure of probability that an alpha particle will be deflected by a given angle during an interaction with an atomic nucleus. Cross section is typically denoted ( sigma) and is expressed in units of area, more specifically in barns. In a way, it can be thought of as the size of the object that the excitation must hit in order for the process to occur, but more exactly, it is a parameter of a stochastic process. In classical physics, this probability often converges to a deterministic proportion of excitation energy involved in the process, so that, for example, with light scattering off of a particle, the cross section specifies the amount of optical power scattere ...
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Schrödinger Equation
The Schrödinger equation is a linear partial differential equation that governs the wave function of a quantum-mechanical system. It is a key result in quantum mechanics, and its discovery was a significant landmark in the development of the subject. The equation is named after Erwin Schrödinger, who postulated the equation in 1925, and published it in 1926, forming the basis for the work that resulted in his Nobel Prize in Physics in 1933. Conceptually, the Schrödinger equation is the quantum counterpart of Newton's second law in classical mechanics. Given a set of known initial conditions, Newton's second law makes a mathematical prediction as to what path a given physical system will take over time. The Schrödinger equation gives the evolution over time of a wave function, the quantum-mechanical characterization of an isolated physical system. The equation can be derived from the fact that the time-evolution operator must be unitary, and must therefore be generated by t ...
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Integral Equation
In mathematics, integral equations are equations in which an unknown Function (mathematics), function appears under an integral sign. In mathematical notation, integral equations may thus be expressed as being of the form: f(x_1,x_2,x_3,...,x_n ; u(x_1,x_2,x_3,...,x_n) ; I^1 (u), I^2(u), I^3(u), ..., I^m(u)) = 0where I^i(u) is an integral operator acting on ''u.'' Hence, integral equations may be viewed as the analog to differential equations where instead of the equation involving derivatives, the equation contains integrals. A direct comparison can be seen with the mathematical form of the general integral equation above with the general form of a differential equation which may be expressed as follows:f(x_1,x_2,x_3,...,x_n ; u(x_1,x_2,x_3,...,x_n) ; D^1 (u), D^2(u), D^3(u), ..., D^m(u)) = 0where D^i(u) may be viewed as a differential operator of order ''i''. Due to this close connection between differential and integral equations, one can often convert between the two. For examp ...
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Raytheon
Raytheon Technologies Corporation is an American multinational aerospace and defense conglomerate headquartered in Arlington, Virginia. It is one of the largest aerospace and defense manufacturers in the world by revenue and market capitalization. In addition, it is one of the largest providers of intelligence services. Raytheon Technologies manufactures aircraft engines, avionics, aerostructures, cybersecurity, guided missiles, air defense systems, satellites, and drones. The company is also a large military contractor, getting a significant portion of its revenue from the U.S. government. The company is the result of the merger of equals between the aerospace subsidiaries of United Technologies Corporation (UTC) and the Raytheon Company, which was completed on April 3, 2020. Before the merger, UTC spun off its non-aerospace subsidiaries Otis Elevator Company and Carrier Corporation. UTC is the nominal survivor of the merger but it changed its name to Raytheon Technologies ...
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Biographical Memoirs Of The National Academy Of Sciences
The ''Biographical Memoirs of the National Academy of Sciences'' has been published by the United States National Academy of Sciences since 1877 and presents biographies of selected members. This series of annual volumes (often abbreviated ''BMNAS''), and the analogous British ''Biographical Memoirs of Fellows of the Royal Society'', are "important examples of biographical serials".. The entries in the series are written by an academy member familiar with the subject's work and are written after the subject's death. Each entry includes a biography, photo, and a copy of the subject's signature A signature (; from la, signare, "to sign") is a handwritten (and often stylized) depiction of someone's name, nickname, or even a simple "X" or other mark that a person writes on documents as a proof of identity and intent. The writer of a .... Recent biographies from this series have also been made available online.. References External links * United States National Acade ...
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Doctor Of Philosophy
A Doctor of Philosophy (PhD, Ph.D., or DPhil; Latin: or ') is the most common Academic degree, degree at the highest academic level awarded following a course of study. PhDs are awarded for programs across the whole breadth of academic fields. Because it is an earned research degree, those studying for a PhD are required to produce original research that expands the boundaries of knowledge, normally in the form of a Thesis, dissertation, and defend their work before a panel of other experts in the field. The completion of a PhD is often a requirement for employment as a university professor, researcher, or scientist in many fields. Individuals who have earned a Doctor of Philosophy degree may, in many jurisdictions, use the title ''Doctor (title), Doctor'' (often abbreviated "Dr" or "Dr.") with their name, although the proper etiquette associated with this usage may also be subject to the professional ethics of their own scholarly field, culture, or society. Those who teach at ...
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Power Dividers And Directional Couplers
Power dividers (also power splitters and, when used in reverse, power combiners) and directional couplers are passive devices used mostly in the field of radio technology. They couple a defined amount of the electromagnetic power in a transmission line to a port enabling the signal to be used in another circuit. An essential feature of directional couplers is that they only couple power flowing in one direction. Power entering the output port is coupled to the isolated port but not to the coupled port. A directional coupler designed to split power equally between two ports is called a hybrid coupler. Directional couplers are most frequently constructed from two coupled transmission lines set close enough together such that energy passing through one is coupled to the other. This technique is favoured at the microwave frequencies where transmission line designs are commonly used to implement many circuit elements. However, lumped component devices are also possible at lower ...
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Electromagnetic Spectrum
The electromagnetic spectrum is the range of frequencies (the spectrum) of electromagnetic radiation and their respective wavelengths and photon energies. The electromagnetic spectrum covers electromagnetic waves with frequencies ranging from below one hertz to above 1025 hertz, corresponding to wavelengths from thousands of kilometers down to a fraction of the size of an atomic nucleus. This frequency range is divided into separate bands, and the electromagnetic waves within each frequency band are called by different names; beginning at the low frequency (long wavelength) end of the spectrum these are: radio waves, microwaves, infrared, visible light, ultraviolet, X-rays, and gamma rays at the high-frequency (short wavelength) end. The electromagnetic waves in each of these bands have different characteristics, such as how they are produced, how they interact with matter, and their practical applications. There is no known limit for long and short wavelengths. Extreme ultr ...
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Microwave
Microwave is a form of electromagnetic radiation with wavelengths ranging from about one meter to one millimeter corresponding to frequencies between 300 MHz and 300 GHz respectively. Different sources define different frequency ranges as microwaves; the above broad definition includes both UHF and EHF (millimeter wave) bands. A more common definition in radio-frequency engineering is the range between 1 and 100 GHz (wavelengths between 0.3 m and 3 mm). In all cases, microwaves include the entire SHF band (3 to 30 GHz, or 10 to 1 cm) at minimum. Frequencies in the microwave range are often referred to by their IEEE radar band designations: S, C, X, Ku, K, or Ka band, or by similar NATO or EU designations. The prefix ' in ''microwave'' is not meant to suggest a wavelength in the micrometer range. Rather, it indicates that microwaves are "small" (having shorter wavelengths), compared to the radio waves used prior to microwave te ...
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K Band (IEEE)
The IEEE K-band is a portion of the radio spectrum in the microwave range of frequencies from 18 to 27-Gigahertz (GHz). The range of frequencies in the center of the K-band between 18- and 26.5-GHz is absorbed by water vapor in the atmosphere due to its resonance peak at 22.24-GHz, . Therefore these frequencies experience high atmospheric attenuation and cannot be used for long distance applications. For this reason the original K-band has been split into three bands, Ka-band, K-band, and Ku-band as detailed below. The K stands for Kurz which stems from the German word for short. Subdivisions Because of the water vapor absorption peak in the center of the band, the IEEE K-band is conventionally divided into three sub-bands: * Ku-band: K-under band, 12–18-GHz, mainly used for satellite communications, direct-broadcast satellite television, terrestrial microwave communications, and radar, especially police traffic-speed detectors. * K-band 18–27-GHz: Due to the 22-GHz wate ...
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