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Basics of Quantum Mechanics Dragica Vasileska Professor Arizona State University
Basics of Quantum Mechanics Dragica Vasileska Professor Arizona State University

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Orthogonal polynomials, special functions and mathematical physics

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... Two identical objects, one neutral and the other with a charge of +4.0 C, are brought into contact and then separated to distance of 0.25 m. Calculate the magnitude of the electrostatic force between the two charged objects. 0.14 N a. 0.58 N ...
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... has 1 MeV or more as energy, as is typical in nuclear phenomena, the energy is large compared to the binding energy of the electrons in the atom. To a first approximation, matter can beseen as a mixture of free electrons and nuclei at rest. The charged particle will feel the electromagnetic fields o ...
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... potential source of gamma rays during these experiments. The joining of an electron and positron produces gamma rays, with the frequency of the gamma rays based on the speed of the joining process. For unknown reasons, the ‘joining process’ of the smashed proton’s positive charge with the electron i ...
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Renormalization



In quantum field theory, the statistical mechanics of fields, and the theory of self-similar geometric structures, renormalization is any of a collection of techniques used to treat infinities arising in calculated quantities.Renormalization specifies relationships between parameters in the theory when the parameters describing large distance scales differ from the parameters describing small distances. Physically, the pileup of contributions from an infinity of scales involved in a problem may then result in infinities. When describing space and time as a continuum, certain statistical and quantum mechanical constructions are ill defined. To define them, this continuum limit, the removal of the ""construction scaffolding"" of lattices at various scales, has to be taken carefully, as detailed below.Renormalization was first developed in quantum electrodynamics (QED) to make sense of infinite integrals in perturbation theory. Initially viewed as a suspect provisional procedure even by some of its originators, renormalization eventually was embraced as an important and self-consistent actual mechanism of scale physics in several fields of physics and mathematics. Today, the point of view has shifted: on the basis of the breakthrough renormalization group insights of Kenneth Wilson, the focus is on variation of physical quantities across contiguous scales, while distant scales are related to each other through ""effective"" descriptions. All scales are linked in a broadly systematic way, and the actual physics pertinent to each is extracted with the suitable specific computational techniques appropriate for each.
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