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Ð I T Ố ƯỢ NG VÀ PH ƯƠ NG PHÁP NGHIÊN C U C H C Ứ Ơ Ọ . a) C h c c đi n: do Newton xây d ng qua công ơ ọ ổ ể ự trình “Nh ng nguyên lý toán h c c a tri t h c t nhiên” ữ ọ ủ ế...
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’s abstract quantum mechanics 210. ’s contributions to quantum mechanics 4. ’s general theory of relativity 60, 96. ’s special theory of relativity 58. density of the electric field 142 density of the magnetic field 142 theorem (electromagnetic) 163 theorem (mechanics) 27, 28 conservation 50. Faraday’s induction law Fermat’s variational principle of the. Fick’s laws (heat diffusion) 306, 307 fictitious...
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All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965,...
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30.2 Fine Structure of the p-Levels. 30.3 Vector Model of the Quantization of the Angular Momentum 257 31 Ritz Minimization. 34.1 Heitler and London’s Theory of the H 2 -Molecule. Why is the O 2 -Molecule Paramagnetic. 36.2 The Aharonov-Bohm Effect. 40.4 Solutions of the Diffusion Equation. 41.1 Introduction: Work. 41.5 The Heat Capacity Differences C p − C V...
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mentioned, a different viewpoint is also possible, and it is better to keep an open mind on these matters than to fix our ideas unnecessarily.. Finally, the problem of planetary motion dating back to the time of New- ton where one must in principle distinguish between the inertial mass m t. entering (2.2) and a gravitational mass m s ,...
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20 4 Mechanics of the Damped and Driven Harmonic Oscillator Thus far we have only dealt with the free harmonic oscillator.. 1) We now consider a forced harmonic oscillator, restricting ourselves at first to the simple periodic “driving force”. However, due to the superposition principle this is no real restriction, since almost every driving force f (t) can be written...
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Kepler’s Problem. 6.2 Kepler’s Three Laws of Planetary Motion. 1) The planets orbit the central star, e.g., the sun, on an elliptical path, where the sun is at one of the two foci of the ellipse.. 2) The vector from the center of the sun to the planet covers equal areas in equal time intervals.. 3) The ratio T 2...
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The differential cross-section is defined as the ratio d dΩ (2) σ : d (2) σ. At a large distance beyond the target, a fraction of the particles enters a counter, where they are recorded. The aperture of the counter corresponds to scattering angles in the interval (ϑ, ϑ + dϑ), i.e., to the corresponding solid angle element. The differential...
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Poisson Brackets 53 In the second case the sum of the braced terms yields a definition for the so-called Poisson brackets:. For the three components of the above-mentioned Runge-Lenz vector F. it can be shown that with the particular (but most important) Hamilto- nian for the Kepler problem (i.e., with -A/r potentials) the Poisson brackets [ H , F ]...
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Here all masses m α can be replaced by 1 in the original equation, if one adds a symbol. Thus we have. The diagonal values (“eigenvalues”) of the matrix are positive (with the above- mentioned exception), so they can be written as ω α 2 , with ω α ≥ 0, for α = 1. 3N , including the six...
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We should mention in this context that modifications of this problem fre- quently appear in written examination questions, in particular the problem of the transition from rolling motion down an inclined segment to a subsequent horizontal motion, i.e., on a horizontal plane segment, and we also mention the difference between gliding and rolling motions (see below).. As an additional problem...
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If one fixes the values of the independent conserved quantities, then in 2f - dimensional phase-space (with the canonical phase-space variables p 1. This applies, e.g., to so-called three-body problems, and it would also apply to the asymmetric heavy top, as mentioned above, or to the double pendulum. It is no coincidence that in the usual textbooks 1 little attention...
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which has, as for “flat” Minkowski spaces, one eigenvalue of one sign and three eigenvalues of the opposite sign.. Further details which would lead to Einstein’s general theory of relativity, will not be treated here, although the effects of curvature of space and time not only play a part in present-day astrophysics, e.g., in the neighborhood of neutron stars and...
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Maxwell’s theory lies at the heart of these technologies, and his equations at the heart of the theory.. Exercises relating to this part of the book (originally in German, but now with English translations) can be found on the internet, [2].. Several introductory textbooks on theoretical electrodynamics and as- pects of optics can be recommended, in particular “Theoretical Electrody- namics”...
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where γ is the gravitational constant, is otherwise similar to Coulomb’s law in electrostatics.. For a distribution of point charges, the electric field E ( r ) generated by this ensemble of charges can be calculated according to the principle of su- perposition. (17.5) This principle, which also applies for Newton’s gravitational forces, is often erroneously assumed to be self-evident....
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Proof of the above statements is again based on Gauss’s integral theorem, according to which (with E n. (17.28) However. where the change of sign reflects that, e.g., the outer normal of V 1 is an inner normal of S. (17.29). The solution of the corresponding Neumann problem (i.e., not U , but Q is given) is also essentially unique...
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one obtains. (17.49) i.e., there are no (“true”) magnetic charges at all, but only magnetic dipoles.. The above relation is the second Maxwell equation, which is again essen- tially based on experimental experience.. Using these relations, the magnetic field H in the absence of electric currents, can be derived from a magnetic potential φ m , which is calculated from...
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b) In the dipole case one would obtain outside the (fictitious) dipole film the equivalent result. (18.10) Proof of the equivalence of the two results proceeds analogously to Stokes’s theorem, but since it is somewhat difficult in detail, we only give an outline in a footnote 3 . The diagram illustrates a typical section of the magnetic field lines produced...
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160 19 Maxwell’s Equations I: Faraday’s and Maxwell’s Laws. The quantity R is the complex a.c. Capacitive resistances (negatively imaginary) correspond to a pair of capacitor plates, together with the letter C. Thus with the ansatz U C (t. Inductive resistances (positively imaginary) are represented by a solenoid symbol, together with the letter L. (The induced voltage drop in the...
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170 20 Maxwell’s Equations II: Electromagnetic Waves. 20.5 Hertz’s Oscillating Dipole (Electric Dipole Radiation, Mobile Phones). r , (20.14). (If B ( r , t) obeys Maxwell’s equations, then so does E ( r , t) and vice versa, in accordance with (20.14).). the retarded vector potential has the following form, which is explicitly used in equation (20.14):. In particular,...