TAILIEUCHUNG - Basic Theoretical Physics: A Concise Overview P19

Basic Theoretical Physics: A Concise Overview P19. 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. | Introduction Wave Equations Group and Phase Velocity 181 where n y E p is the refractive index2. In optically dense light-transmitting media . glass or water n is significantly 1 which gives rise to the well-known phenomenon of refraction described by Snell s law sin oq n2 sin a2 n1 This expression describes the refraction of light rays at a plane boundary between a vacuum with refractive index n 1 or in practice air and an optically denser medium with n2 1. The angle of incidence from the vacuum is o . The refractive index n is thus related both to the relative dielectric constant of the material r and also to the relative permeability pr3. This also means that generally n depends on the wavenumber k and frequency w. The above relation for dielectric and or permeable matter follows from Maxwell s equations in the absence of charges and currents . for p j 0 div r oE q 0 divB 0 dB B dE curlE curl j Applying the operator curl to the third and fourth equations together with the identity curl curlv grad divv V2v we obtain the following wave equations v2 -1- dt M E 0 and v2 dt 2 B 0 cm J cm where cm see below is the velocity of a stationary electromagnetic wave in the considered medium. Similar wave equations occur in other cases . for transverse sound waves shear waves transverse phonons in solid state physics it is only necessary to replace E and cB by the transverse displacements of the atoms from their rest positions and the velocity of light cm by the transverse sound velocity c S which in metals is of the order of 103 m s . With these replacements one obtains the same wave equation in totally different contexts. There are also longitudinal sound waves compression waves4 longitudinal phonons with a significantly higher sound velocity c g 2 In some mainly artificial materials both e and p are negative . also n. These so-called left-handed materials have unusual optical properties. 3 To avoid any misunderstanding here we explicitly use the lower

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