gst a theoretical overview

Basic Theoretical Physics: A Concise Overview P43 potx

Ngày tải lên : 06/07/2014, 17:20

... field approximation (bi-linearized) of a Hamiltonian 334 mean field approximations 405, 408 measurable quantities (“observables”) in quantum mechanics 215 measurable quantities (observables) in quantum ... 313 magnetism 271 magnetization M = J /μ0 314 magnetocaloric effect 372 magnetostatics 119, 139 magnons (spin-wave quanta) 185, 379, 399, 402 main-sequence stars 388 MAPLE, MATHEMATICA 161 Markoff ... external force 23 external torque 24 extraordinary versus ordinary beam (uniaxial birefringence) 191 extremal paths (Einstein) 96 Fahrenheit, Ráumur (or Reamur) e 303 far-field range 170, 173 Faraday’s...

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Basic Theoretical Physics: A Concise Overview P44 pps

Ngày tải lên : 06/07/2014, 17:20

... volumes, are already available (see, for example, [1]) Exercises closely adapted to the book can be found on one of the authors websites [2], and these may be an additional help We have laid emphasis ... 41 Lagrange Formalism I: Lagrangian and Hamiltonian 8.1 The Lagrangian Function; Lagrangian Equations of the Second Kind 8.2 An Important Example: The ... 18.5 Gyromagnetic Ratio and Spin Magnetism 145 145 146 147 148 19 Maxwell’s Equations I: Faraday’s and Maxwell’s Laws 19.1 Faraday’s Law of Induction and the Lorentz...

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Basic Theoretical Physics: A Concise Overview P2 pptx

Ngày tải lên : 06/07/2014, 17:20

... phenomena such as “chaos” are treated brieﬂy in a separate chapter (Chap 12) As far as possible, only elementary formulae have been used in the presentation of relativity 1.2 General Remarks on Space ... by material properties and physical events It is also assumed that b) time runs separately as an absolute quantity; i.e., it is assumed that all clocks can be synchronized by a signal transmitted ... countries This quantity is deﬁned as the gravitational force acting on a kg mass in standard earth gravity (in Paris where the archive kilogram was deposited) At that time the quantity force was considered...

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Basic Theoretical Physics: A Concise Overview P3 pdf

Ngày tải lên : 06/07/2014, 17:20

... Third Axiom (“Action and Reaction ”) a) As a consequence of equating the inertial and gravitational masses in Newton’s equation F (r) = ms · G(r) it follows that all bodies fall equally fast ... oscillation”, and afterwards the seemingly rather special, but actually quite general “periodically driven oscillation”, and also the seemingly very special, but actually equally general so-called “ballistically ... mass); n and τ are the osculating normal and the tangential unit vectors, respectively A one-dimensional treatment follows Finally, as already alluded to above, the quanties τ (t), n(t), R(t), and...

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Basic Theoretical Physics: A Concise Overview P5 potx

Ngày tải lên : 06/07/2014, 17:20

... usual three conservation laws for energy, angular momentum, and linear momentum for a planetary system The additional conservation law only applies for potentials of the form A/ r (as well as A ... inversesquare law of force: Fr (r) = A , r2 where A > (attractive interaction), while the parameter p and the angular momentum L are related to A by: L2 p= A m 6.5.3 Hyperbolas; Comets Equation ... gravitational ﬁeld Newton’s systematic analysis of Kepler’s laws (leading him to the important idea of a central gravitational force) follows below; but ﬁrstly we shall discuss the reverse path,...

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Basic Theoretical Physics: A Concise Overview P6 pot

Ngày tải lên : 06/07/2014, 17:20

... Schematic diagram on diﬀerential scattering cross-sections A particle enters the diagram from the left on a path parallel to the x-axis at a perpendicular distance b (the so-called “impact parameter”; ... vanish, and since δq(t) is arbitrary, the action functional S becomes extremal for the actual orbit, qv (t) ≡ q(t), 48 Lagrange Formalism I: Lagrangian and Hamiltonian Fig 8.1 Hamilton’s variational ... hypersurface element 46 Lagrange Formalism I: Lagrangian and Hamiltonian also included (see below) The fact that the Lagrangian contains the diﬀerence, and not the sum of the kinetic and potential...

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Basic Theoretical Physics: A Concise Overview P7 pot

Ngày tải lên : 06/07/2014, 17:20

... frame called the aether) However, the transformation between diﬀerent inertial frames must be made via a Lorentz transformation not a Galilean transformation As a consequence, as already mentioned6 ... thus always shorter than the time interval dt measured in any other frame This means for example that a co-moving clock transported in an aeroplane around the earth, ticks more slowly than an earth-based ... be mainly calculated from the scalar potential Φ, since A E = −gradΦ − ∂t The main content of the relativistic invariance of Maxwell’s theory is, as we shall only mention, that Φ and A can be...

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Basic Theoretical Physics: A Concise Overview P8 ppt

Ngày tải lên : 06/07/2014, 17:20

... considerably, as follows: Assume that all parameters reﬂect this left-right symmetry, i.e., the Lagrangian L shall be invariant against permutation of the indices j = and j = 3, such that the ... axial vector : For example, a right-handed rotation around the unit vector n with positive angular velocity ϕ is identical ˙ to a rotation, also right-handed, around (−n) with negative angular ... the parameter variation leading to the building up of the oscillation amplitude is ωP = · ω0 for the above example This mechanical example is actually most instructive In fact, the equations are...

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Basic Theoretical Physics: A Concise Overview P9 pdf

Ngày tải lên : 06/07/2014, 17:20

... εγ ωγ , i.e., along one diagonal axis they are attracted, but along the other diagonal axis there is repulsion, and the orbit runs far away from the axis where it started The appearance of hyperbolic ... space R3 (ω), but in the dual space R3 (L) by the relation 2Trot = L2 α Θα α=1 Instead of the angular velocity ω, the angular momentum L is now central In fact, L and ω are not parallel to each ... branches again (for ϑ = 0: upwards and downwards) into dissipationless axle bearings, which support a third rotation axis, 3, related to the direction e3 (i.e., the ﬁgure axis), with rotation angle...

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Basic Theoretical Physics: A Concise Overview P10 pptx

Ngày tải lên : 06/07/2014, 17:20

... global inertial frames as demanded by Mach exist, but only “free falling” local inertial frames, or more accurately: relative to the given gravitating bodies freely moving local inertial frames ... depends in x a nontrivial manner on the distribution of the gravitating masses, and It was again Einstein, who postulated in 1910 that the equality should actually be replaced by an identity As to the ... some years after he had formulated his special theory of relativity, was led to the postulate that a) no principal diﬀerence exists between gravitational and inertial forces (Einstein’s equivalence...

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Basic Theoretical Physics: A Concise Overview P11 pptx

Ngày tải lên : 06/07/2014, 17:20

... which are measured and mapped by geophysicists, e.g., in mineral prospecting As usual, for didactical reasons we distinguish between the inertial mass mt and the gravitational mass ms , although ... geographical latitude The gravitational weight of a kilogram increases towards the poles 100 – 14 Accelerated Reference Frames (aii) The terms ∝ ω in the second equation and the north anomaly ... totality of all stars But as mentioned above it was only Einstein, who, some years later, cut the “Gordian knot” by stating that only local inertial frames exist, thus solving in an elegant way...

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Basic Theoretical Physics: A Concise Overview P12 pdf

Ngày tải lên : 06/07/2014, 17:20

... , 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, however, ... Similar considerations apply to gravitational forces; in fact, “gravitational mass” could also be termed “gravitational charge”, although an essential diﬀerence from electric charges is that inter ... theorem: triangulating a 2d-surface in space As an example, the surface z = xy is triangulated (i.e., paved) by a grid of small squares If all the squares are oriented in the same way as the outermost...

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Basic Theoretical Physics: A Concise Overview P13 ppt

Ngày tải lên : 06/07/2014, 17:20

... a short mathematical section on polar coordinates Hitherto we have always written vectors, e.g., dr, as triples of three orthogonal Cartesian coordinates We shall now adopt general curvilinear ... formula for orthogonal curvilinear coordinates, which can be proved by elementary considerations on source densities: divE = a1 a2 a3 a2 a3 ∂E1 ∂E2 ∂E3 + a3 a1 + a1 a2 ∂u1 ∂u2 ∂u3 (17.27) Capacitors; ... that although Maxwell’s equations are based on experimental observations Therefore they should not really be regarded as universal laws or axioms, which are – as it were – self-evident or valid...

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Basic Theoretical Physics: A Concise Overview P14 pps

Ngày tải lên : 06/07/2014, 17:20

... plate capacitor (with plate area F and plate separation d), a spherical capacitor (with inner radius R and outer radius R + ΔR), and for a cylindrical capacitor (with length L and inner radius ... the quadrupole 136 17 Electrostatics and Magnetostatics tensor can be changed by the addition of an arbitrary diagonal tensor, qi,k → qi,k + a · δi,k , without any change in the potential As a result, ... amongst other reasons, because it allows one immediately to accept a solution (found or guessed by any means available) as the only solution One should not underestimate the practical importance...

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Basic Theoretical Physics: A Concise Overview P15 pptx

Ngày tải lên : 06/07/2014, 17:20

... arbitrary gradient field to A, then curlA is not changed at all A so-called gauge transformation: A → A := A + gradf (r) , (18.5) with arbitrary f (r), implies curlA ≡ curlA , since curl gradf ≡ Therefore, ... expressions are fundamental and will be used later Firstly, we shall start with a capacitor with dielectric material of dielectric constant ε between the plates Let us transport an infinitesimal amount ... equations (17.46) and (17.48) one can always calculate the electrostatic field E(r) and the magnetostatic field H(r) of an electrically or magnetically polarized system, at every sampling point r;...

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Basic Theoretical Physics: A Concise Overview P16 pps

Ngày tải lên : 06/07/2014, 17:20

... thus realize that Faraday’s law of induction (19.3), which appears so simple, embodies a great deal of experimental information In addition we may already surmise at this point that Maxwell’s ... I: Faraday’s and Maxwell’s Laws 19.4 Applications: Self-inductance and Mutual Inductances; Transformers; Complex Resistances; Alternating-current Resonance Circuit a) Inductance Consider a solenoid ... cannot stop in the interspace: curls must always continue (a diagram is recommended here!) As with Faraday’s law of induction, the integral form of the fourth Maxwell equation is again somewhat...

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Basic Theoretical Physics: A Concise Overview P17 potx

Ngày tải lên : 06/07/2014, 17:20

... This can simultaneously serve as an introduction to MAPLE In fact, it may be helpful to illustrate resonance phenomena using mathematical computer tools such as MAPLE or MATHEMATICA See for example ... Potentials I: D’Alembert’s Equation For given electromagnetic ﬁelds E(r, t) and B(r, t) one can satisfy the second and third Maxwell equations, i.e., Gauss’s magnetic law, divB = 0, and Faraday’s law ... the d’Alembert equations, i.e., with vanishing r.h.s of the equation (and ∝ δ(r)) Of special importance among these solutions are planar electromagnetic waves and spherical waves 20.3 Planar Electromagnetic...

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Basic Theoretical Physics: A Concise Overview P18 pptx

Ngày tải lên : 06/07/2014, 17:20

... that Maxwell’s equations, which are not invariant under a Galilean transformation, are invariant w.r.t a Lorentz transformation – as it was later called – in which space and time coordinates are ... Details can be found in (20.21).6 For magnetic multipole radiation the results are similar 20.8 Relativistic Invariance of Electrodynamics We have already seen in Part I that classical mechanics ... 20.6 Magnetic Dipole Radiation; Synchrotron Radiation For vanishing charges and currents Maxwell’s equations possess a symmetry which is analogous to that of the canonical equations of classical...

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Basic Theoretical Physics: A Concise Overview P19 ppt

Ngày tải lên : 06/07/2014, 17:20

... optically uniaxial crystals, in the latter case with optically biaxial crystals We have now arrived at the phenomenon of birefringence, and as a simple example we shall consider a linearly polarized ... terms analogously to the eikonal ansatz ) leads to the so-called Hamilton-Jakobi equations of classical mechanics, viz (gradS)2 + V (r) ≡ E 2m The Hamilton-Jakobi equation contains the totality ... wave quantities considered7 , we try to solve this Neglecting the vectorial character of the electromagnetic ﬁeld is already an approximation, the so-called scalar approximation This can already...

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Basic Theoretical Physics: A Concise Overview P20 potx

Ngày tải lên : 06/07/2014, 17:20

... larger19 The signal would thus be alienated and disguised by the above long-wavelength fringes In our example from seismology, however, a disadvantage can be turned into an advantage, because from the ... wavelength λ, but in the near-ﬁeld range they vary on much shorter scales 21.4.2 Fraunhofer Diﬀraction at a Rectangular and Circular Aperture; Optical Resolution In the following we shall treat ... coworkers The hologram, using no lenses at all (!), measures the blackening function of a photographic plate, which is illuminated simultaneously by an object wave and a reference wave As a consequence,...

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