By David A. Mazziotti
An updated account of this state-of-the-art learn in a constant and comprehensible framework, of particular 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 lecture room in addition to a useful source for figuring out the severe developments within the box.
Read Online or Download Advances in Chemical Physics, Reduced-Density-Matrix Mechanics: With Application to Many-Electron Atoms and Molecules (Volume 134 PDF
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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
It is then merely a question of counting to show that the energy, E, of the system is given by E ¼ hcjHjci ¼ 12 NðKD2 Þ Taking a hint from the treatment of helium by Hylleraas, I realized that one merely had to choose D2 ð12; 10 20 Þ to minimize the above expression for ﬁxed N and with K appropriate for any quantum system of N identical fermions to obtain the ground-state energy level. To impress physicists one needed to do this for a system more complicated than helium. So I tried to ﬁnd the ground state of lithium assuming that my guess for D2 ð12; 10 20 Þ was restricted only by the conditions that it be antisymmetric in 12 and 10 20 and change these pairs under complex conjugation.
Rosina, J. K. Percus, L. J. Kijewski, and C. Garrod, Reduced density matrices of energy eigenstates. J. Math. Phys. 10, 1761–1763 (1969). 20. M. Rosina and C. Garrod, The particle–hole matrix: its connection with the symmetries and collective features of the ground state. J. Math. Phys. 10, 1855 (1969). 21. C. Garrod, M. V. Mihailovic´, and M. Rosina, The variational approach to the two-body density matrix. J. Math. Phys. 16, 868–874 (1975). 22. M. Rosina and C. Garrod, The variational calculation of reduced density matrices.
Rosina and M. V. Mihailovic´, The determination of the particle–hole excited states by using the variational approach to the ground state two-body density matrix, in International Conference on Properties of Nuclear States, Montreal 1969, Les Presses de l’Universite´ de Montreal, 1969. 26. M. Bouten, P. Van Leuven, M. V. Mihailovic´, and M. Rosina, A new particle–hole approach to collective states. Nucl. Phys. A202, 127–144 (1973). 27. M. Bouten, P. Van Leuven, M. V. Mihailovic´, and M. Rosina, Two exactly soluble models as a test of the Hermitian operator method.