Kummer, Hans

The search was first pursued in a series of conferences organized by Bob Erdahl, Hans Kummer, the late Vedene Smith, Jr., and myself. However, many others have been involved, notably Prof. Valdemoro and her colleagues in Spain, Prof. Nakatsuji and his associates in Japan, and since completing his Ph.D. at Harvard, Prof. Mazziotti in Chicago. 

Others (e.g., Fukashi Sasaki s upper bound on eigenvalues of 2-RDM [2]). Claude Garrod and Jerome Percus [3] formally wrote the necessary and sufficient A -representability conditions. Hans Kummer [4] 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 [5] was very successful for three-electron atoms and Richard Hall and H. Post [6] for three-nucleon nuclei (if assuming a fully attractive nucleon-nucleon potential). 

A beautiful month on Lake Qntario in a very friendly atmosphere. John Coleman, Bob Erdahl, Claude Garrod, Richard Hall, Hans Kummer, J. Lindenberg, R. McWeeny, Yngve Qhrn, David Peat, Mitja Rosina, Mary-Beth Ruskai, Darwin Smith, George Warsket, Antonio Ciampi, Ernest Davidson, and others discussed A-representability, the interpretation of RDMs, and other unsolved problems. 

B = 0. Essential for understanding the present approach is the basic paper [3] of Hans Kummer. 

Recall that in his Theorems 3 and 4 Hans Kummer [3] defined a contraction operator, L, which maps a linear operator on A-space onto an operator on p-space and an expansion operator, E, which maps an operator on p-space onto an operator on A-space. Note that the contraction and expansion operators are super operators in the sense that they act not on spaces of wavefunctions but on linear spaces consisting of linear operators on wavefunction spaces. If the two-particle reduced Hamiltonian is defined as... 

In one sense, research in theoretical chemistry at Queen s University at Kingston originated outside the Department of Chemistry when A. John Coleman came in 1960 as head of the Department of Mathematics. Coleman took up Charles Coulson s challenge150 to make the use of reduced density matrices (RDM) a viable approach to the N-electron problem. RDMs had been introduced earlier by Husimi (1940), Lowdin (1955), and McWeeny (1955). The great attraction was that their use could reduce the 4N space-spin coordinates of the wavefunctions in the variational principle to only 16 such coordinates. But for the RDMs to be of value, one must first solve the celebrated N-repre-sentability problem formulated by Coleman, namely, that the RDMs employed must be derivable from an N-electron wavefunction.151 This constraint has since been a topic of much research at Queen s University, in the Departments of Chemistry and Mathematics as well as elsewhere. A number of workshops and conferences about RDMs have been held, including one in honor of John Coleman in 1985.152 Two chemists, Hans Kummer [Ph.D. Swiss Federal Technical... 

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