Download Repetitorium - Theoretische Physik by Armin Wachter PDF
By Armin Wachter
Die überarbeitete und aktualisierte zweite Auflage des Repetitorium Theoretische Physik enthält den kanonischen Lehrstoff der Theoretischen Physik, der in den ersten 6 Semestern an deutschen Universitäten gelehrt wird. Zwei junge theoretische Physiker bieten den Prüfungsstoff für Vordiplom, Zwischenprüfung, Diplom und Staatsexamen in prägnanter und argumentativ stringenter Darstellung. Von der klassischen Mechanik über Elektrodynamik, Quantenmechanik und Statistische Physik/Thermodynamik werden alle Themen in einer axiomatisch-deduktiven Darstellung behandelt und durch Übungen mit Lösungen sowie Zusammenfassungen gefestigt. Das Buch eignet sich sowohl als begleitendes Lehrbuch als auch zum Wiederholen und Strukturieren von bereits vertrautem Lehrstoff und überbrückt somit die Kluft zwischen umfangreichen Lehrbüchern und reinen Formelsammlungen. Dieses Repetitorium der Theoretischen Physik wird insbesondere all jene begeistern, die sich in der Prüfungsvorbereitung befinden und den Lehrstoff noch einmal im Zusammenhang durchgehen wollen.
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X; yÞ appears as x ¼ xðsÞ þ y0 ðsÞh; y ¼ yðsÞ À x0 ðsÞh: s y h x FIGURE 17 The near-surface curvilinear coordinates system (s, h). ð1:54Þ 28 Integral Equations Method in Electrostatics The curvilinear coordinate system (s,h) is orthogonal, and the square of the infinitesimal length element is dl2 ¼ ð1 þ k0 ðsÞhÞ2 ds2 þ dh2 ; ð1:55Þ where k0 ðsÞ ¼ y00 ðsÞx0 ðsÞ À x00 ðsÞy0 ðsÞ is the local curvature coefficient. The Laplace operator transformed to the curvilinear coordinates (s, h) reads as 0 D¼ @2 1 @2 k0 @ k0 h @ À ; þ þ @h2 ð1 þ k0 hÞ2 @s2 1 þ k0 h @h ð1 þ k0 hÞ3 @s ð1:56Þ 0 where k0 ðsÞ ¼ y000 ðsÞx0 ðsÞ À ðsÞy0 ðsÞ.
9 may help to trace a large number of trajectories and determine both the transparency coefficient and the scattering function of a grid cell. Our aim here is to show that taking into account some features specific to the problem in question may advance the calculations. The mathematical model of a fine-structure grid represents an infinite periodical array of cells. The direct use of the classic 3D BEM immediately restricts the case to only a few adjacent grid cells involved in the calculation and complimented with two additional finite-size electrodes generating the electric field on both sides of the grid.
2 15 0. 0. 4 25 0. 6 35 0. 40 0. 8 45 0. 0 FIGURE 28 The singularity index versus the reduced permittivity ratios in the case of three dielectric wedges, the faces of which intersect at right angles. As above, no exact solution to this equation exists for all possible values of the apex angle b. Therefore, here we restrict ourselves to the numerical results shown in Figure 29 and investigate some limiting cases. As in the case above, the singularity index lies in the range 0 g < 1=2. The asymptotic behavior may be easily analyzed in the limits of high permittivity (e >> 1) and small apex angle (b << 1).