By David A. Mazziotti
An updated account of this state-of-the-art learn in a constant and comprehensible framework, of certain curiosity to specialists in different parts of digital constitution and/or quantum many-body idea. it's going to serve both good as a self-contained advisor to studying approximately diminished density matrices both via self-study or in a school room in addition to a useful source for figuring out the severe developments within the box.
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Additional resources for Advances in Chemical Physics, Reduced-Density-Matrix Mechanics: With Application to Many-Electron Atoms and Molecules (Volume 134
Claude Garrod and Jerome Percus  formally wrote the necessary and sufﬁcient N-representability conditions. Hans Kummer  provided a generalization to inﬁnite spaces and a nice review. Independently, there were some clever practical attempts to reduce the three-body and four-body problems to a reduced two-body problem without realizing that they were actually touching the variational 2-RDM method: Fritz Bopp  was very successful for three-electron atoms and Richard Hall and H. Post  for three-nucleon nuclei (if assuming a fully attractive nucleon–nucleon potential).
Blok and A. E. L. ), North-Holland, Amsterdam, 1974. 29. M. V. Mihailovic´ and M. Rosina, Particle–hole states in light nuclei, in Proceedings of the International Conference on Nuclear Self-Consistent Fields, Trieste 1975 (G. Ripka and M. ), North-Holland, Amsterdam, 1975, p. 37. 18 mitja rosina 30. M. Rosina, Application of the two-body density matrix of the ground state for calculations of some excited states. Int. J. Quantum Chem. 13, 737–742 (1978). 31. M. Rosina and P. Van Leuven, Density-matrix approach to wave-packet dynamics.
Lifting conditions 2. T1 =T2 conditions E. Convex set of two-particle reduced Hamiltonian matrices 1. Convex Set of N-representable 2-RDMs 2. Positivity and the 1-RDM 3. Positivity and the 2-RDM 4. Strength of positivity conditions F. Spin and spatial symmetry adaptation 1. Spin adaptation and S-representability G. Open-shell molecules III. Semideﬁnite programming IV. Applications V. A Look Ahead Acknowledgments References I. INTRODUCTION In 1927 Landau  and von Neumann  introduced the density matrix into quantum mechanics.
Advances in Chemical Physics, Reduced-Density-Matrix Mechanics: With Application to Many-Electron Atoms and Molecules (Volume 134 by David A. Mazziotti