J. Keller, P. Weinberger:

"The use of quadratic forms in the calculation of ground state electronic structures";

Journal of Mathematical Physics,47(2006), 0835051 - 08350512.

There are many examples in theoretical physics where a fundamental quantity can

be considered a quadratic form ρ=Σiρi=¦Ψ¦² and the corresponding linear form

Ψ=ΣiΨi is highly relevant for the physical problem under study. This, in particular,

is the case of the density and the wave function in quantum mechanics. In the study

of N-identical-fermion systems we have the additional feature that Ψ is a function

of the 3N configuration space coordinates and is defined in three-dimensional real

space. For many-electron systems in the ground state the wave function and the

Hamiltonian are to be expressed in terms of the configuration space (CS), a replica

of real space for each electron. Here we present a geometric formulation of the CS,

of the wave function, of the density, and of the Hamiltonian to compute the electronic

structure of the system. Then, using the new geometric notation and the

indistinguishability and equivalence of the electrons, we obtain an alternative computational

method for the ground state of the system. We present the method and

discuss its usefulness and relation to other approaches.

http://aleph.ub.tuwien.ac.at/F?base=tuw01&func=find-c&ccl_term=AC05938330

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