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chapter 4
chapter 4

... At the source the electron is being emitted as particle and is experimentally detected as a electron which is absorbed by an individual atom in the fluorescent plate In between, we must interpret the electron in the form of a wave. The double slits change the propagation of the electron wave so that ...
Slide 1
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... • S is “real” in that it has classical analogs in mechanics (intrinsic angular momentum) and electrodynamics (magnetic moment)  = gsS N • T has no classical analog; it is a quantum mechanical vector, literally “like spin” (iso = ‘like’), so it follows the same addition rules as S, L, J, etc... ...
Review Notes on Angular Momentum, Correspondence Between
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Symmetries of a system
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Flat spin connections in the Teleparallel equivalent of General
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Multiphoton ionization of hydrogen in parallel simulations
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Mathematics and the Twelve-Tone System: Past
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Force and Motion Demos - California State University, Long Beach
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PowerPoint version 0.4MB - School of Mathematics | Georgia
PowerPoint version 0.4MB - School of Mathematics | Georgia

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... At t1 we insert a partition in the center of the box, where the wavefunction is zero, so that the expectation value for the energy remains completely unaltered. This is highly idealized, to be sure, creating many technical questions. For example, given the quantum mechanical uncertainty relations, o ...
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Renormalization group



In theoretical physics, the renormalization group (RG) refers to a mathematical apparatus that allows systematic investigation of the changes of a physical system as viewed at different distance scales. In particle physics, it reflects the changes in the underlying force laws (codified in a quantum field theory) as the energy scale at which physical processes occur varies, energy/momentum and resolution distance scales being effectively conjugate under the uncertainty principle (cf. Compton wavelength).A change in scale is called a ""scale transformation"". The renormalization group is intimately related to ""scale invariance"" and ""conformal invariance"", symmetries in which a system appears the same at all scales (so-called self-similarity). (However, note that scale transformations are included in conformal transformations, in general: the latter including additional symmetry generators associated with special conformal transformations.)As the scale varies, it is as if one is changing the magnifying power of a notional microscope viewing the system. In so-called renormalizable theories, the system at one scale will generally be seen to consist of self-similar copies of itself when viewed at a smaller scale, with different parameters describing the components of the system. The components, or fundamental variables, may relate to atoms, elementary particles, atomic spins, etc. The parameters of the theory typically describe the interactions of the components. These may be variable ""couplings"" which measure the strength of various forces, or mass parameters themselves. The components themselves may appear to be composed of more of the self-same components as one goes to shorter distances.For example, in quantum electrodynamics (QED), an electron appears to be composed of electrons, positrons (anti-electrons) and photons, as one views it at higher resolution, at very short distances. The electron at such short distances has a slightly different electric charge than does the ""dressed electron"" seen at large distances, and this change, or ""running,"" in the value of the electric charge is determined by the renormalization group equation.
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