By Arthur Cox

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9. The electron states within the bands are delocalized and possess the translational invariance of the crystal. 30) where uk (r) is a function that has the periodicity of the lattice. 30 are modulated plane waves. Each electronic band has a different envelope function uk (r) which retains some of the atomic character of the states from which the band was derived. 5 Characteristic optical physics in the solid state 21 Optical transitions can occur between the electronic bands if they are allowed by the selection rules.

In the free atoms, the magnetic levels are degenerate. We must apply a magnetic field to split them by the Zeeman effect. However, the magnetic levels can be split even without applying an external magnetic field in a crystal. The details of the way the levels split are determined by the symmetry class of the crystal. 20 Introduction known effect in atomic physics. Free atoms are spherically symmetric and have no preferred directions. The symmetry can be broken by applying an external magnetic or electric field which creates a preferred axis along the field direction.

Let R1 and R2 be respectively the reflectivities of the front and back surfaces, and α be the absorption coefficient of the medium. (a) By adding the intensities of the beams transmitted after multiple reflections to the intensity of the beam transmitted after the first pass, show 26 Exercises that the transmission of the plate is given by: T = (1 − R1 )(1 − R2 ) e−αl . e. 77 and αl = 0. (c) Discuss the implications of the results of part (b). incident light transmitted light reflected light Fig. 10 Multiple reflections in a parallel-sided plate.

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A system of optical design by Arthur Cox


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