By Abello T.P.
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Additional info for Absorption of Ultra-Sonic Waves by Hydrogen and Carbon Dioxide
Sample text
The direct product of a higher dimensional species with itself will be reducible and will contain the totally symmetric representation. The direct product of more than two representations can be obtained simply by forming the direct product of the first two representations and multiplying the result in series with all others. These direct product representations are applied in molecular orbital theory to show the symmetry of the wave function, to express selection rules in spectroscopy, and for other applications.
7) Let's choose the proton as the origin of our coordinate system. In principle, we should have chosen the center of mass of the system as the origin, but because the proton is ca. 1840 times heavier than the electron, our choice is still acceptable. ) Since the Coulomb field has spherical symmetry, the calculations are simpler if we use spherical polar coordinates instead of Cartesians. 3. 8) x=r·cos8 If we express the wave function in this new coordinate system, we find that it can now be given as a product of two functions: an r-dependent radial function, R(r), and an angular part, 48 QUANTUM CHEMISTRY: FUNDAMENTALS TO APPLICATIONS z y ..................
A. M. Dirac, Proc. Roy. Soc. (London) A 118, 315 (1928), Anderson, 1. , Mathematics for Quantum Chemistry. A. Benjamin, New York, 1966. This is a small and useful book about the calculus of orthogonal functions and the algebra of vector spaces. Bransden, B. H. and C. 1. Joachain, The Physics of Atoms and Molecules. Longman, New York, 1991. Contains the experimental background and the elements of quantum mechanics. Eisberg, R. and R. Resnick, Quantum Physics of Atoms. Molecules. Solids. Nuclei and Particles, 2nd ed.
Absorption of Ultra-Sonic Waves by Hydrogen and Carbon Dioxide by Abello T.P.
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