TAILIEUCHUNG - Basic Theoretical Physics: A Concise Overview P26

Basic Theoretical Physics: A Concise Overview P26. This concise treatment embraces, in four parts, all the main aspects of theoretical physics (I . Mechanics and Basic Relativity, II. Electrodynamics and Aspects of Optics, III. Non-relativistic Quantum Mechanics, IV. Thermodynamics and Statistical Physics). It summarizes the material that every graduate student, physicist working in industry, or physics teacher should master during his or her degree course. It thus serves both as an excellent revision and preparation tool, and as a convenient reference source, covering the whole of theoretical physics. It may also be successfully employed to deepen its readers’ insight and. | 256 30 Addition of Angular Momenta By straightforward but rather lengthy methods or more generally by group theory2 this can be shown to be exactly possible if J is taken from the following set J e L S L S - 1 . L - S . Furthermore MJ must be one of the 2 J 1 integral or half-integral values -J J 1 . J and MJ ML MS. The coefficients in are called Clebsch-Gordan coefficients. . Unfortunately there are many different conventions in use concerning the formulation of the coefficients. Fine Structure of the p-Levels Hyperfine Structure Without the spin-orbit interaction the p-levels 1 1 of the outermost electron of an alkali atom are sixfold since including spin one has 2 x 21 1 6 states. Under the influence of the spin-orbit interaction the level splits into a fourfold p3-level . with j 1 2 with positive energy shift AE and a twofold p 1 -level . with j 1 2 with an energy shift which is twice as large but negative 2AE the center of energy of the two levels is thus conserved. This so-called fine structure splitting gives rise for example to the well-known sodium D-lines in the spectrum of a sodium salt. Analogously to the fine structure which is is based on the coupling of L and S of the electrons dTLfine k r L S there is an extremely weak hyperfine structure based on the coupling of the total angular momentum of the electronic system J with the nuclear spin I to the total angular momentum of the atom F J I . We have Hhyperfine C ö r J I where the factor c is proportional to the magnetic moment of the nucleus and to the magnetic field produced by the electronic system at the location of the nucleus. In this way one generates . the well-known 21 cm line of the neutral hydrogen atom which is important in radio astronomy. 2 See . Gruppentheorie und Quantenmechanik lecture notes in German 2 Vector Model of the Quantization of the Angular Momentum 257 Vector Model of the Quantization of the Angular Momentum The above-mentioned mathematical

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