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possible total reflection against air at appropriate angles of incidence For such effects observed with minerals and inorganic glasses, the term wststiwhlen was coined The strong influence of this range on the reflectance spectra is obvious from Fig 64-5 where simulations for normal and oblique incidence are presented Reflectance at 0" incidence (Eq 64-15) is primarily determined by the absorption band ( k ) accomplished on the low-wavenumber side by the contribution from the refractive index The spectral shape is similar to a band rather than to a dispersion feature Also at large angles of incidence, the reflectance spectra for s-polarized and p-polarized radiation are characterized by bands These are definitely shifted away from the resonance frequency and into the reststrahlen range, and they are correspondingly broadened.



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The upper or contravariant symbol A( ) that appears in this operator-valued integral is highly nonunique, but will be chosen as the simplest one Three basic matrices generate the Jordan algebra 15) of all real symmetric 2 ~ 2 matrices They are the identity matrix I d , the symbol of which is trivially the

10% 03% 03% 02% 01% 03% 19% 06% 01% 03%

15) A Jordan algebra is an algebra (not necessarily associative) over a eld whose multiplication is commutative and satis es the Jordan identity: (x y )x 2 = x(y x 2 )





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The high-wavenumber limit of such a reflectance band is clearly defined by the point where n equals unity (a N 1090 cm I ) , ie the refractive index of ambient air The other occurrence of n = 1 close to 50 is accompanied by such high absorption, that considerable reflectance is observed at least for the s-polarized component The reflectance band for ppolarized radiation is limited to short wavenumbers where the condition for the Brewster angle is met This condition is met a second time within the reflection band This does not become evident in the reflectance spectrum due to the related high value of k To some extend the existence of a reststrahlen range (12 < 1 ) defines a strong oscillator Within this range another remarkable situation is found where E' = 0 According to Eq 64-13 this means n = k.

1 1

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This matrix is obviously positive since, for any nonzero vector |v in the plane, we 1 have v |P ( )|v = d | v | |2 > 0 POVMs are important partners of resolutions of the unity, as will be seen at different places in this book

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This condition refers to the so-called longitudinal optical (LO) mode and cannot be observed with bulk material Its excitation by a transversal electromagnetic wave should be forbidden However, when a thin film of a reststrahlen material is deposited on a highly reflecting substrate such as metal, a guided wave can be excited at this particular wavenumber This phenomenon is known as Berreman effect (Berreman, 1963) and renders possible to identify and quantify surface layers of some nanometers thickness - roughly ten thousand times thinner than the infrared wavelength used (Weidner and Roseler, 1992) The outstanding gain in sensitivity is reached since radiation is travelling a long distance within the film rather than just traversing it An experimental example is given in Fig 64-7..

The resolution of the identity (34) provided by the coherent states is the key for transforming any abstract or concrete realization of the quantum states into the Fock Bargmann analytical one Let | =

(314)

RCS s command-line options are cumulative, as you might expect, and RCS does a good job of disallowing incompatible options. To check out and lock a specific revision of howdy.c, you would use a command such as co -l -r2.1 howdy.c. Similarly, ci -u -r3 howdy.c checks in howdy.c, assigns it revision number 3.1, and deposits a read-only revision 3.1 working file back into your current working directory. The following example creates revision 2.1 of howdy.c. Make sure you have checked out and changed howdy.c somehow before executing this command.

be a vector in the Hilbert space H of quantum states in some of its realizations Its scalar product with a Schr dinger coherent state (chosen preferably to be a standard coherent state to avoid the Gaussian weights) reads as the power series

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