Advances in Chemical Physics, Special - download pdf or read online

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Positivity and the 1-RDM A quantum system of N particles may also be interpreted as a system of ðr À NÞ holes, where r is the rank of the one-particle basis set. The complementary nature of these two perspectives is known as the particle hole duality [13, 44, 45]. Even though we treated only the N-representability for the particles in the formal solution, any p-hole RDM must also be derivable from an ðr À NÞ-hole density matrix. While the development of the formal solution in the literature only considers the particle reduced Hamiltonian, both the particle and the hole representations for the reduced Hamiltonian are critical in the practical solution of Nrepresentability problem for the 1-RDM [6, 7].

N-REPRESENTABILITY 7 sympathetically the diversity of religious and political experiences in Europe, Asia, Africa, and North America. But, what I had not expected, it also gave me a chance to meet distinguished scientists such as Hadamard, the French mathematician made famous for his discussion of the prime number theorem; Werner Heisenberg, with whom I enjoyed two evenings in Goettingen during the week in which I attended the funeral of Planck; W. Threlfall, the English topologist, who, protected by his Nazi student, Seifert, lived safely in Germany throughout the War during part of which he was housed inside a huge airplane factory in a splended cottage provided in case the Minister of the Luftwaffe came to inspect the factory, which he never did.

Post, Proc. Phys. Soc. A69, 936 (1956); A79: 819 (1962); A90: 381 (1967); A91: 16 (1967). 7. M. V. Mihailovic´ and M. Rosina, Excitations as ground state variational parameters. Nucl. Phys. A130, 386 400 (1969). 8. M. Rosina, Transition amplitudes as ground state variational parameters, in Reduced Density Matrices with Applications to Physical and Chemical Systems (A. J. Coleman and R. M. ), Queen’s Papers in Pure and Applied Mathematics No. 11, Queen’s University, Kingston, Ontario, 1967, p. 369.

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