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First-order semidefinite programming for the two-electron treatment of many-electron atoms and molecules

David A. Mazziotti (2007)

ESAIM: Mathematical Modelling and Numerical Analysis


The ground-state energy and properties of any many-electron atom or molecule may be rigorously computed by variationally computing the two-electron reduced density matrix rather than the many-electron wavefunction. While early attempts fifty years ago to compute the ground-state 2-RDM directly were stymied because the 2-RDM must be constrained to represent an N-electron wavefunction, recent advances in theory and optimization have made direct computation of the 2-RDM possible. The constraints in...

Fundamental solutions for Dirac-type operators

Swanhild Bernstein (1996)

Banach Center Publications

We consider the Dirac-type operators D + a, a is a paravector in the Clifford algebra. For this operator we state a Cauchy-Green formula in the spaces C 1 ( G ) and W p 1 ( G ) . Further, we consider the Cauchy problem for this operator.

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