Award Abstract #0545895
CAREER: Toward Direct Numerical Solution of the Multiparticle Schrodinger Equation

NSF Org:	DMS Division of Mathematical Sciences
Initial Amendment Date:	July 28, 2006
Latest Amendment Date:	July 28, 2006
Award Number:	0545895
Award Instrument:	Standard Grant
Program Manager:	Thomas F. Russell DMS Division of Mathematical Sciences MPS Directorate for Mathematical & Physical Sciences
Start Date:	August 1, 2006
Expires:	July 31, 2011 (Estimated)
Awarded Amount to Date:	$400000
Investigator(s):	Martin Mohlenkamp mjm@math.ohiou.edu (Principal Investigator)
Sponsor:	Ohio University 108 CUTLER HL ATHENS, OH 45701 740/593-2857
NSF Program(s):	APPLIED MATHEMATICS
Field Application(s):	0000099 Other Applications NEC
Program Reference Code(s):	OTHR, 1187, 1045, 0000
Program Element Code(s):	1266

ABSTRACT

The multiparticle Schrodinger equation is the basic governing equation in quantum mechanics, and thus the foundation for much of chemistry and physics. A tremendous amount of effort, over several decades, has gone into approximating its solutions, but high-quality numerical solutions have proved elusive. Recently-developed mathematical tools for computing in high dimensions have revealed a new path toward such solutions, which this project will explore. Such solutions will enable accurate computation of chemical and physical properties of molecules and materials, and thus have an impact on many problems in chemistry, physics, biology, and materials science.

This research will occur in the Department of Mathematics at Ohio University, a state university located in the Appalachian region of southeastern Ohio, with a renewed commitment to strengthening its research at all levels. The research group will include both undergraduate and graduate students, who will contribute to this project and develop valuable skills in computational mathematics. The students will also learn about the research process and develop their skills at communicating mathematics.

PUBLICATIONS PRODUCED AS A RESULT OF THIS RESEARCH

Gregory Beylkin, Jochen Garcke, and Martin J. Mohlenkamp. "Multivariate Regression and Machine Learning with Sums of Separable Functions," SIAM Journal on Scientific Computing, v.31(3), 2009, p. 1840.

Gregory Beylkin, Martin J. Mohlenkamp, and Fernando Perez. "Preliminary results on approximating a wavefunction as an unconstrained sum of Slater determinants," Proceedings in Applied Mathematics and Mechanics, v.7, 2007, p. 1010301.

Gregory Beylkin, Martin J. Mohlenkamp, and Fernando Perez. "Approximating a wavefunction as an unconstrained sum of Slater determinants," Journal of Mathematical Physics, v.49, 2008, p. 032107.

Mohlenkamp, Martin J.. "A Center-of-Mass Principle for the Multiparticle Schrodinger Equation," Journal of Mathematical Physics, v.51, 2010, p. 022112.

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