Donald Kouri


Donald Kouri
Cullen Distinguished University Chair
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

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.