Basic Theoretical Physics: A Concise Overview P23 pdf

... (26.1) The harmonic oscillator is important inter alia because a potential energy V (x) in the vicinity of a local minimum can almost always be approximated by a parabola (which is the characteristic ... that V (r) should be rota- tionally invariant. Next, the usual ansatz for stationary states is made: ψ(r,t)=u(r) · e −iEt/ . Then, in spherical coordinates a product ansatz (separati...

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... r and m s refer to the planet, and R and M s to the central star (“sun”), while γ is the gravitational constant. Here the [gravitational] masses play the role of gravitational charges, similar ... “active” and “passive” gravitational masses are equal (see the end of the preceding sec- tion), i.e., on the one hand, a body with an (active) gravitational charge M s generates a gravitational...

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... 11.3. TheimportanceoftheEuler angles goes far beyond theoretical mechanics as demonstrated by the technical importance of the Cardani suspension. Fig. 11.3. The figure illustrates a so-called Cardani sus- pension, ... axis the ω-lines are hyperbolas, ∝  ε α ω 2 α − ε γ ω 2 γ  , i.e., along one diagonal axis they are attracted, but along the other diagonal axis there is repulsion, and the...

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... of q 1 q 2 , whereas the gravitational force is always attractive, since “gravitational charges” always have the same sign, while the gravitational constant leads to attraction (see (17.4)). Certainly, ... (17.3) Similar considerations apply to gravitational forces; in fact, “gravitational mass” could also be termed “gravitational charge”, although an essential difference from electric charges...

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... decayed from a state without any angular momentum. We assume that the decay products are two particles, which travel diametrically away from each other in opposite di- rections, and which are always correlated ... measuring apparatus on the r.h.s. prepares a spin state with a value  2 in a certain direction, then a simultanous measurement on the opposite side, performed with a si...

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... ap- proximation, usually called mean field approximation, by replacing a sum of bilinear operators by a self-consistent temperature-dependent linear ap- proximation in which fluctuations are neglected. ... we have seen that thermal fluctuations are im- portant in the neighborhood of the critical temperature of a second-order phase transition, i.e. near the critical temperature of a liqui...

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... 331 equations 163 mean field approximation (bi-linearized) of a Hamiltonian 334 mean field approximations 405, 408 measurable quantities (“observables”) in quantum mechanics 215 measurable quantities ... 402 main-sequence stars 388 MAPLE, MATHEMATICA 161 Markoff chain 412 mass defect 104 mathematical (versus physical) pendulum 75 Maxwell ’s displacement current 153, 156 ’s equations in Gaussia...

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... Vector as an Additional Conserved Quantity 39 7 The Rutherford Scattering Cross-section 41 8 Lagrange Formalism I: Lagrangian and Hamiltonian 45 8.1 The Lagrangian Function; Lagrangian Equations of ... Current Loops and their Equivalent Magnetic Dipoles 149 18.5 GyromagneticRatioandSpinMagnetism 151 19 Maxwell’s Equations I: Faraday’s and Maxwell’s Laws 153 19.1 Faraday’s Law of Induction and...

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... Experiment; LiquefactionofAir 319 41.7 Adiabatic ExpansionofanIdealGas 324 42 Phase Changes, van der Waals Theory and Related Topics 327 42.1 VanderWaals Theory 327 42.2 Magnetic Phase Changes; The Arrott Equation. ... Quantum Mechanics: Retrospect and Prospect 293 38 Appendix: “Mutual Preparation Algorithm” for Quantum Cryptography 297 Part I Mechanics and Basic Relativity 4 1 Space and Ti...

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... not just a universal number, but proportional to the mass M of the respective central star.) As already mentioned, Kepler’s second law is also known as the law of equal areas and is equivalent to ... the planet covers equal areas in equal time intervals. 3) The ratio T 2 /a 3 ,whereT is the time period and a the major principal axis of the ellipse, is constant for all planets (of the so...

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