Donald Kouri
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Donald Kouri
Cullen Distinguished Professor
Ph.D., University of Wisconsin, 1965
M.S., University of Wisconsin, 1962
B.A., Oklahoma Baptist University, 1960
Department of Chemistry
University of Houston
Houston, Texas 77204-5003
Office: 606B - SR1
Phone: 713.743.3245
kouri@uh.edu
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Theoretical and Mathematical Chemistry
Fundamental quantum theory; generalized
coherent states; quantum theory of atomic and molecular collisions;
few body problems; approximate methods for calculating cross sections,
theory of reactive scattering, nonequilibrium statistical mechanics;
real-time Feynman path integral studies; wavepacket treatments of
quantum dynamics; digital signal processing; wavelet theory; multiresolution
analysis.
We
are continuing to carry out research in the formal and computational
aspects of molecular collision dynamics. Our current focus is on combining
our recently developed time-independent wavepacket formulation of
reactive scattering with various approximations. The basic idea is
to use our "divide-and conquer" approach (using absorbing
and emitting potentials as formulated by my former student John Zhang,
and modified by myself) so that different appropriate approximations
can be used in the various separate dynamical regions (e.g., the entrance
channel, strong-interaction region, and various exit channels). A
key part of the research is the use of different coordinates in each
region so that the equations are most nearly separable in each region.
This will facilitate the choice of the optimal approximation in each
region.
A
second major area of research is in what might be called "mathematical
chemistry and physics". We have developed a new approach to
functional approximations called the "distributed approximating
functionals" (DAFs) and used them to solve a variety of both
linear and nonlinear partial differential equations. We also have
used them to develop new "filters" for denoising experimental
and computational data. We shall be continuing this research, looking
at a broad range of problems generally known as "digital signal
processing", in addition to an enormous range of areas, including
imaging, data compression, pattern recognition, neural networks,
wavelet theory, etc.
The
third major area of research we are currently pursuing is in the
fundamentals of quantum theory. Of particular interest is a new
generalization of the Heisenberg uncertainty principle, so as to
include the idea of multiresolution analysis. This is important
for nonlinear optics (e.g., preparation of optimal coherent light
pulses), Bose-Einstein condensation and confinement of material
particles, quantum computing, and many other areas. It has led to
the development of generalized Gaussian and coherent quantum states.
These promise to be important both theoretically and experimentally.
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