Winston theory

As can be seen from formula (2.44) which defines the dielectric tensor without spatial dispersion, nonzero contributions to the tensor ij come from those mechanical excitons, for which the dipole matrix elements Po o/t of an elementary cell are nonzero. 

The dipole moment operator of the total crystal is given by 

by making use of the formula (2.4) which gives the crystal wavefunction for the ground state, then using the formula (2.8), which for k = 0 gives the wavefunction of a Coulomb exciton with k = 0 in the excitonic band //, we obtain 

The expression for Po oM in the case of mechanical excitons has the same form (2.57), but the functions u ),(()) must be replaced by u (0), obtained by neglecting the effects of the long-wavelength field. Since the operator P° is transformed like a polar vector, and the wavefunction To is invariant under all crystal symmetry transformations, the matrix element (2.57) will be nonzero only for those excitonic states whose wavefunctions are transformed like the components of a polar vector. If, for example, the function ToM transforms like the x-component of a polar vector, the vector Po o will be parallel to the x-axis. Thus the symmetry properties of the excitonic wavefunctions determine the polarization of a light wave which can create a given type of exciton. In the above example only a light wave polarized in the x-direction will be absorbed, obviously, if we restrict the consideration to dipole-type absorption. In a similar way, for example, the quadrupole absorption in the excitonic region of the spectrum can be discussed (for details see, for example, 8 in (12)). 

As we have shown above, the energies of mechanical excitons for k = 0 do not depend on the direction of k. This property simplifies the group-theoretical classification of the states of mechanical excitons and will be used below. 

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HarF67 Harary, F. A proof of Polya s enumeration theorem. A seminar in graph theory. (F. Harary, ed.) Holt, Rinehart and Winston, New York (1967) 21-24. 

PMO Theory of Organic Chemistry Plenum NY, 1975 Zimmerman, H.E. Quantum Mechanics for Organic Chemists Academic Press NY, 1975 Borden, W.T. Modem Molecular Orbital Theory for Organic Chemists Prentice-Hall Englewood Cliffs, NJ, 1975 Dewar, M.J.S. The Molecular Orbital Theory of Organic Chemistry McGraw-Hill NY, 1969 Liberies, A. Introduction to Molecular Orbital Theory Holt, Rinehart, and Winston NY, 1966. 

Viscous Flows The Practical Use of Theory Stuart Winston Churchill... 

State Physics, Holt, Rinehan and Winston, New York, 1976. Three other introductions to the field, ones that I think are pedagogically effective and accessible to chemists, are Harrison, W. A. Solid State Theory, Dover, New York, 1980. Harrison, W. A. Elecnonic Structure and the Properties of Solids, W. H. Freeman, San Francisco, 1980 Altman, S. L. Band Theory of Metals, Pergamon Press, New York, 1970. 

Harris, S., An Introduction to the Theory of the Boltzmann Equation, Holt, Rinehart and Winston, Inc., New York, 1971. 

Schutz, W. C., FIRO A Three-Dimensional Theory of Interpersonal Behaviour. New York Holt, Rinehart and Winston, 1958, with the instrument and scoring available from Whetton, D. A., and K. S. Cameron, Developing Management Skills. Glenview, IL Scott Foresman, 1984, 80. 

Barlow, R. E., and Proschan, F. (1975), Statistical Theory of Reliability and Life Testing, Holt, Rinehart Winston, New York. 

Schutz, W. C. (1958). FIRO A three dimensional theory of interpersonal behavior. New York Holt, Rinehart Winston. 

Under the evolution of the earth and the climate system, we will simply understand the historical development from earliest times until the present. Theories for how the atmosphere and ocean formed must begin with an idea of how the earth itself originated (Kasting 1993). An understanding of our atmosphere and the climate system is incomplete without going into the past. The farther backward you can look the farther forward you can see Winston Churchill). 

R. Barlow, F. Proschan Statistical theory of reliability and life testing. Holt, Rinehart Winston, 1975... 

Fillmore, C. J. The case for case. In E. Bach R. T. Harms Eds., Universals of linguistic theory. New York Holt, Rinehart, Winston, pp. 1-90.1968. 

Naylor, A. W., and G. R. Sell, Linear Operator Theory in Engineering and Science, Holt Rinehart and Winston, New York, 1971. 

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