Generator coordinate method

Van Leuven, P., and Lathouwers, L. (1980), The Generator Coordinate Method in Molecular Physics, in Quantum Dynamics of Molecules, R. G. Woolley (Ed.), Plenum, New York. 

We present a new mapping procedure from fermion onto boson spaces. The procedure is based on the Generator Coordinate Method. We show an application of this technique to systems of nucleons moving in a single j-orbit. The extension of this microscopic investigation to many j-orbit systems is also examined. 

The procedure we are going to expose is based on the Generator Coordinate Method (GCM). The GCM looks for solutions of the Schrodinger equation of the form... 

Mito, Y. and Kamimura, M. (1976). The generator coordinate method for composite-particle scattering based on the Kohn-Hulth6n variational principle,... 

It has also been pointed out that there is an interpretation to our theory based upon the generator coordinate approach [44 6]. A close scrutiny of Lathouwers et al. paper shows that the present approach can be embedded into the methodology of the generator coordinate method (GCM), as it was pointed out by one referee. The postulate PI ensures the existence of a set of fixed nuclei so that the GCM, initially thought for... 

The Generator Coordinate Method for Atomic and Molecular Systems Revision and Further Developments... 

The generator coordinate method (GCM), as initially formulated in nuclear physics, is briefly described. Emphasis is then given to mathematical aspects and applications to atomic systems. The hydrogen atom Schrodinger equation with a Gaussian trial function is used as a model for former and new analytical, formal and numerical derivations. The discretization technique for the solution of the Hill-Wheeler equation is presented and the generator coordinate Hartree-Fock method and its applications for atoms, molecules, natural orbitals and universal basis sets are reviewed. A connection between the GCM and density functional theory is commented and some initial applications are presented. 

Osvaldo and I certainly became friends. We later met many times, in Uppsala, Norway, Florida (where 1 had also the privilege to meet Professor Slater 1 believe he and a few others - Hartree, Fock, Bom, Oppenheimer - set the foundations in the 1930s of what we now call quanmm chemistry). I remember specially when, in Rio de Janeiro, during the 6th Escola Latinoamericana de Quimica Teorica in 1988, Osvaldo had very stimulating words on our first results with the generator coordinate method, which I review below. 

Wheeler and collaborators [3], in the context of nuclear physics, showed at that time that the limit in the variational procedure potential itself was not reached. Indeed, the Rayleigh-Ritz (RR) variational scheme teaches us how to obtain the best value for a parameter in a trial function, i.e., exponents of Slater (STO) or Gaussian (GTO) type orbital, Roothaan or linear combination of atomic orbitals (LCAO) expansion coefficients and Cl coefficients. Instead, the generator coordinate method (GCM) introduces the Hill-Wheeler (HW) equation, an integral transform algorithm capable, in principle, to find the best functional form for a given trial function. We present the GCM and the HW equation in Section 2. 

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